3D Spherical Harmonic Invariant Features for Sensitive and Robust Quantitative Shape and Function Analysis in Brain MRI

by

Ashish Uthama

B. E. (Electronics and Communication Engineering), Visvesvaraya Technological University, 2003

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OF

Master of Applied Science

in

THE FACULTY OF GRADUATE STUDIES

(Electrical & Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

October 2007

© Ashish Uthama, 2007

Abstract

A novel framework for quantitative analysis of shape and function in magnetic resonance

imaging (MRI) of the brain is proposed. First, an efficient method to compute invariant

spherical harmonics (SPHARM) based feature representation for real valued 3D

functions was developed. This method addressed previous limitations of obtaining unique

feature representations using a radial transform. The scale, rotation and translation

invariance of these features enables direct comparisons across subjects. This eliminates

need for spatial normalization or manually placed landmarks required in most

conventional methods [1-6], thereby simplifying the analysis procedure while avoiding

potential errors due to misregistration. The proposed approach was tested on synthetic

data to evaluate its improved sensitivity. Application on real clinical data showed that this

method was able to detect clinically relevant shape changes in the thalami and brain

ventricles of Parkinson’s disease patients. This framework was then extended to generate

functional features that characterize 3D spatial activation patterns within ROIs in

functional magnetic resonance imaging (fMRI). To tackle the issue of intersubject

structural variability while performing group studies in functional data, current state-of-

the-art methods use spatial normalization techniques to warp the brain to a common atlas,

a practice criticized for its accuracy and reliability, especially when pathological or aged

brains are involved [7-11]. To circumvent these issues, a novel principal component

subspace was developed to reduce the influence of anatomical variations on the

functional features. Synthetic data tests demonstrate the improved sensitivity of this

approach over the conventional normalization approach in the presence of intersubject

variability. Furthermore, application to real fMRI data collected from Parkinson’s disease

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patients revealed significant differences in patterns of activation in regions undetected by

conventional means. This heightened sensitivity of the proposed features would be very

beneficial in performing group analysis in functional data, since potential false negatives

can significantly alter the medical inference. The proposed framework for reducing

effects of intersubject anatomical variations is not limited to functional analysis and can

be extended to any quantitative observation in ROIs such as diffusion anisotropy in

diffusion tensor imaging (DTI), thus providing researchers with a robust alternative to the

controversial normalization approach.

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Table of Contents

Abstract…………………………...………...………………………………………........2

Table of Contents………………...………....…………………………………….…..…4

List of Tables…………………...……..……………………...….…………………..…viii

List of Figures...................................................................................................................9

Statement of Co-authorship............................................................................................xii

1 Thesis Introduction and Summary.............................................................................1

1.1 Thesis Motivations and Objectives......................................................................2

1.2 Principles of Magnetic Resonance Imaging (MRI).............................................3

1.3 Structural Brain MRI...........................................................................................8

1.3.1 Summary of Structural Data Acquired.....................................................................10

1.3.2 MR Image Preprocessing..........................................................................................10

1.3.3 Segmentation of Regions of Interest in the Brain.....................................................12

1.3.4 Quantifying Structural Changes in Brain ROIs........................................................15

1.4 Functional Magnetic Resonance Imaging..........................................................17

1.4.1 Principles of BOLD imaging....................................................................................17

1.4.2 Hemodynamic Response...........................................................................................18

1.4.3 Functional Experiment Setup....................................................................................19

1.4.4 Summary of Functional Data Acquired....................................................................22

1.4.5 fMRI Data Preprocessing..........................................................................................23

1.4.6 Functional Activation Map Generation for Individual Subjects...............................27

1.4.7 Differences in Activation Maps at the Group Level.................................................29

1.5 Thesis Contributions..........................................................................................32

1.5.1 Structural ROI Analysis............................................................................................33

1.5.2 Functional ROI Analysis...........................................................................................34

1.6 Thesis Overview................................................................................................35iv

1.7 References..........................................................................................................37

2 Unique Invariant SPHARM Features for ROI Based Analysis ............................47

2.1 Introduction........................................................................................................47

2.2 Methods.............................................................................................................48

2.2.1 Proposed Invariant SPHARM features.....................................................................49

2.2.2 Statistical Analysis of Features.................................................................................52

2.3 Data and Imaging...............................................................................................53

2.3.1 Synthetic Structural Data Generation.......................................................................53

2.3.2 Real Structural MR Data Acquisition.......................................................................54

2.4 Results and Discussion......................................................................................55

2.4.1 Validation on Synthetic Data....................................................................................55

2.4.2 Analysis of Real MR Structural Data.......................................................................57

2.5 Conclusions........................................................................................................59

2.6 References..........................................................................................................61

3 Detection and Analysis of Anatomical Shape Changes in MRI (PD thalamus)....63

3.1 Background........................................................................................................63

3.2 Results................................................................................................................67

3.3 Discussion..........................................................................................................70

3.4 Conclusions........................................................................................................72

3.5 Methods.............................................................................................................73

3.5.1 MR Imaging at the University of British Columbia.................................................73

3.5.2 MR Imaging at the University of North Carolina.....................................................74

3.5.3 Thalami Shape Analysis...........................................................................................74

3.5.4 Shape Analysis -- Technical Aspects........................................................................75

3.6 Authors' contributions........................................................................................79

3.7 Acknowledgements............................................................................................79

v

3.8 References..........................................................................................................80

4 Detection and Analysis of Anatomical Shape Changes in MRI (PD brain ventricles)..........................................................................................................................87

4.1 Introduction........................................................................................................87

4.2 Methods.............................................................................................................89

4.2.1 Proposed Invariant SPHARM features.....................................................................89

4.2.2 Statistical Analysis of Features.................................................................................93

4.2.3 Automated segmentation of the lateral ventricles.....................................................94

4.3 Data and Imaging...............................................................................................95

4.3.1 Synthetic Structural Data Generation.......................................................................95

4.3.2 Real Structural MR Data Acquisition.......................................................................97

4.4 Results and Discussion......................................................................................97

4.4.1 Validation on Synthetic Data....................................................................................97

4.4.2 Analysis of Real MR Structural Data.......................................................................99

4.5 Conclusions......................................................................................................101

4.6 References........................................................................................................102

5 Extending SPHARM Features to Functional Activation Analysis in fMRI .......105

5.1 Introduction......................................................................................................105

5.2 Methods...........................................................................................................108

5.2.1 Invariant SPHARM-Based Spatial Features...........................................................109

5.2.2 fMRI Analysis Using SPHARM Features..............................................................113

5.2.3 Statistical Group Analysis.......................................................................................115

5.3 Data and Imaging.............................................................................................116

5.3.1 Synthetic fMRI Data...............................................................................................116

5.3.2 fMRI Data of PD Patients.......................................................................................120

5.4 Results and Discussion....................................................................................120

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5.4.1 Validation on Synthetic Data..................................................................................121

5.4.2 Application to Clinical fMRI Data of PD Patients.................................................123

5.5 Conclusions......................................................................................................124

5.6 References........................................................................................................126

6 Validation and Comparisons to Conventional fMRI Analysis Approach ...........129

6.1 Introduction......................................................................................................129

6.2 Methods...........................................................................................................133

6.2.1 Invariant SPHARM-Based Spatial Features...........................................................133

6.2.2 fMRI Group Analysis Using SPHARM Features...................................................138

6.2.3 Statistical Group Analysis.......................................................................................140

6.2.4 ROI Normalization Approach (ROI-N)..................................................................141

6.3 Data and Imaging.............................................................................................142

6.3.1 Synthetic fMRI Data...............................................................................................142

6.3.2 Real fMRI Data.......................................................................................................144

6.4 Results and Discussion....................................................................................147

6.4.1 Validation on Synthetic Data..................................................................................147

6.4.2 Application to Clinical fMRI Data.........................................................................152

6.5 Conclusions......................................................................................................155

6.6 References........................................................................................................156

7 Conclusions and Future Work...............................................................................161

7.1 Technical Contributions...................................................................................161

7.2 Impact on Neuroscience Research...................................................................164

7.3 Future Work.....................................................................................................165

7.4 References........................................................................................................166

8 APPENDIX..............................................................................................................169

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List of Tables

Table 1.1 MR relaxation times for commonly occurring brain tissue.................................9

Table 1.2 MR relaxation time for Oxygenated and Deoxygenated blood.........................18

Table 2.1 Results of pre-drug vs. post-drug analysis.........................................................58

Table 2.2 Results of PD patients vs. controls analysis......................................................59

Table 3.1 Results of volumetric and shape analysis. Numbers indicate the p-values obtained from the permutation test....................................................................................67

Table 4.1 Result of pre-drug vs. post-drug analysis..........................................................99

Table 4.2 Result of comparison between control subjects and PD patients. Values indicated with a * are statistically significant at an alpha value of 0.05............................99

Table 5.1 Permutation test results (p value) of fMRI data analysis from the Parkinson’s disease study (the two groups being ‘before drug’ and ‘after drug’). IG: Internally guided, EG: Externally guided, L: Left, R: Right, CRB: Cerebellar hemisphere, CAU: Caudate. Numbers in bold are statistically significant (alpha = 0.05)............................................122

Table 6.1 Maximum radius of ROIs and the corresponding bandwidth used.................150

Table 6.2 SPHARM analysis of the two frequency tasks. Only ROIS with at least one significant result are shown.............................................................................................151

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List of Figures

Figure 1.1 Gradient fields along the X and Y axes..............................................................7

Figure 1.2 Whole brain images obtained using different relaxation time weighted protocols showing the different tissue contrasts. Left: T1 weighted image. Right: T2

weighted image....................................................................................................................9

Figure 1.3 Left: A raw T1 weighted image (axial slice), notice the noise near the nasal cavity and the eyes (upper part of image). Right: The extracted brain using the combined expectation maximization and geodesic active contour method proposed by Huang et al [33].....................................................................................................................................11

Figure 1.4 Result of anisotropic diffusion filtering on a T1 brain volume (one slice shown)................................................................................................................................12

Figure 1.5 Result of the automatic segmentation of the right brain ventricle. The left venctricle’s binary ROI mask is rendered on orthogonal slices of the subjects T1 image.14

Figure 1.6 The MR-compatible rubber squeeze bulb used in the functional experiment..20

Figure 1.7 Visual feedback given to subject performing the bulb squeezing task. The width of the black horizontal bar reflected the amount of ‘squeezing’ that the bulb recorded. Subjects had to modulate the squeezing action to keep the width within the undulating white pathway..................................................................................................21

Figure 1.8 The stimulus design used for the functional study. The tunnel width shown on the Y axis indicates the width of the undulating pathway shown in Figure 1.7................21

Figure 1.9 Left: A slice from a T1 weighted anatomical scan of a subject. Right: Corresponding slices of T2* scans from functional volumes acquried the duration of the experiment (130 such volumes were collected over a duration of 260 seconds)..............23

Figure 1.10 The process of brain extraction, followed be co-registration of the high resolution T1 anatomical scan to the first functional T2* voume......................................24

Figure 1.11 Motion correction re-aligns the functional volumes in case the subject moves during the time course of acquisition.................................................................................26

Figure 1.12 The process of obtaining subject level statistical parameter maps. The time course of each voxel is statistically compared to an expected response based on the task perfored to obtain a parameter which describes the activation at that voxel. This process is reapeated for all voxels in the brain resulting in the subject level SPM........................28

Figure 1.13 The functional ROIs studied in this thesis. All ROIs shown occur in pairs (in the left and righ brain hemishpheres), only regions in left hemisphere are shown. Indicated ROIs are Prefrontal cortex (PMC), Supplementary motor cortex (SMA),

ix

Primary motor cortex (M1), Caudate (CAU), Putamen (PUT), Thalamus (THA), Cerebellar hemisphere (CER)............................................................................................32

Figure 2.1 (a) The human brain ventricles. The two ventricles would have to be analyzed jointly since the relative orientations might be of importance. One of the spherical shells at r =35 is also shown. (b) The parameterization of the surface at r = 16 (top) and 35 (bottom).............................................................................................................................52

Figure 2.2 (a) Surface rendering of a real left thalamus (top) and right thalamus (bottom) from a PD patient, note the rough edges. (b) Group A synthetic samples (see text) generated with parameter set (2, 5, 10). (c) Group B synthetic sample generated with parameter set (2, 5, 8). Note the realistic looking edges in the synthetic data...................54

Figure 2.3 Plot of the Euclidian distance between the two groups A and B for different values of cb. Distances resulting in a significant difference (alpha = 0.05) between the groups as obtained by the permutation test are indicated with a star. Non-Significant distances are indicated with a dot......................................................................................56

Figure 3.1 The SPHARM-based method for shape determination. The shape to be specified (the thalamus) and two concentric spherical shells are shown. On the right is the intersection between the thalamus and shells as a function of rotation (θ) and azimuth (φ). The rotation angle spans from 0 to 2π radians, and the azimuth angle is from 0 to π radians................................................................................................................................66

Figure 3.2 Two sets typical thalami registered and shown on brain from a PD subject. Note that the registration here is solely for visualization purposes, and is not required for the calculation of shape differences. Also, although the thalami here were first smoothed with a 12mm FWHM Gaussian kernel for visualization purposes, no smoothing was performed for the shape analysis and group comparison..................................................68

Figure 4.1 Intersection of a left brain ventricle with 2 of the 128 shells used to obtain the SPHARM representation. The corresponding sampled surfaces of the two shells are also shown.................................................................................................................................92

Figure 4.2 (a) Surface rendering of a real left thalamus (top) and right thalamus (bottom) from a PD patient, note the rough edges. (b) Group A synthetic samples (see text) generated with parameter set (2, 5, 10). (c) Group B synthetic sample generated with parameter set (2, 5, 8). Note the realistic looking edges in the synthetic data...................95

Figure 4.3 . Plot of the Euclidian distance between the two groups A and B for different values of cb, (ca was fixed at 10 for all points). Distances resulting in a significant difference (alpha = 0.05) between the groups as obtained by the permutation test are indicated with a star. Non-Significant distances are indicated with a dot.........................97

Figure 5.1 A cross section of fMRI activation statistics from the right cerebellar hemisphere of a real subject.............................................................................................116

x

Figure 5.2 A cross section of synthetic fMRI activation statistics for group B from different sets. A pattern consisting of two activation levels corrupted by noise is present, -delta values closer to the functional centre and +delta away from the centre. (a) and (c) represent extreme cases where the pattern present is visually discernible in the presence of noise. (b) and (d) represent very low signal strengths but are still detected by the proposed features. The delta values correspond directly to those in Figure 5.4. A Gaussian noise source of zero mean and σ0 of one was used in the above figures..........117

Figure 5.3 A cross section of fMRI activation statistics for group A synthetic data. Note the absence of a pattern....................................................................................................117

Figure 5.4 Results of the synthetic data experiment. The normalized Euclidian feature distance between groups A and B for each set is plotted against delta for the 3DMI, SPHARM-fs and SPHARM-f features. The black diamond markers represent the distances which yielded significant difference using 3DMI features, the red triangles represent SPHARM-fs features while the blue pentagrams represent SPHARM-f features. The closer the markers are to the zero delta mark, the smaller the failure range, hence better the performance. 3DMI has a failure range of (-1.5, 1.25), SPHARM-fs has a range (-1.1, 1.3), while SPHARM-f features return the best results by being able to discriminate the groups even at every low values of delta (-0.2, 0.7)........................................................119

Figure 6.1 Representing data as a set of spherical functions. Real fMRI data from the right cerebellar hemisphere of a normal subject performing the maximum frequency task (Section III-B) is shown (t>2 for clarity). The shells were obtained using a bandwidth of L=128. The physical values of both angles are non-uniformly spaced (Chebyshev nodes) [19]. The threshold, bandwidth and the depicted transparent ROI boundary are for illustration purposes only.................................................................................................133

Figure 6.2 (a) Cross section of a synthetic pattern injected into the binary mask of a real right cerebellar hemisphere. SNR = 1.204 dB. (b) Cross section of a real fMRI activation statistic map mapped to the same color map...................................................................142

Figure 6.3 False positive rates using SPHARM-f features for various values of the parameter L (Bandwidth). .................................................................................146

Figure 6.4 The average SNR plotted against increasing delta value...............................147

Figure 6.5 Sensitivity of the SPHARM approach. The mean Euclidean distance between the feature vectors of a group with only noise and of another group with increasing SNR is plotted against the SNR. The star and triangle markers denote distance which yielded a p value less 0.05, signifying that the method detected differences between the groups. 148

Figure 6.6 Sensitivity of the ROI-normalization approach. The number of voxels surviving various height thresholds is plotted against the SNR. A cluster size threshold of 4 connected voxels was used in each case. These results were computed from the exact same data generated for Figure 6.5..................................................................................149

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Statement of Co-authorship

All technical content in this thesis were written by Ashish Uthama and edited by his

supervisor, Dr. Rafeef Abugharbieh. Dr. Martin J. McKeown provided the clinical

explanations relevant to the results presented in this thesis. The experimental data were

collected by Samantha J. Palmer, Drew Smith, Cara Slagle, Mechelle Lewis and Xuemei

Huang. All data analysis methods were designed and developed by Ashish Uthama under

the supervision of his supervisor.

xii

1 Thesis Introduction and Summary

Magnetic resonance imaging (MRI) is the most widespread brain imaging technique in

use today. In its basic form, MRI is routinely used in clinical neuroscience to non-

invasively capture anatomical images of the brain for use in detection, diagnosis and

tracking of neurological disorders such as Multiple sclerosis (MS), Parkinson’s, (PD) and

Alzheimer’s disease. Active research in exploring other uses of MR imaging technology

has resulted in exciting new avenues which are distinct research domains in their own

right. One such area is the study of brain function using functional magnetic resonance

imaging (fMRI). The mainstream MRI technique, referred to as structural or anatomical

MRI, provide high resolution 3D images of the brain. This facilitates the study of

(geometric) shape of cortical and subcortical brain structures, e.g. the thalamus or the

ventricles. On the other hand, fMRI, which is currently one of the most actively

researched MR imaging modalities, aims to identify regions of the brain involved in

performing specific actions such as motor or visual tasks. Such knowledge not only

increases our understanding of brain functionality, but also helps neurologists better track

the progress of neurodegenerative diseases and uncover whether, and if so, how the

human brain reacts to disease by employing various compensatory mechanisms [12].

1

1.1 Thesis Motivations and Objectives

One of the main challenges in MR image analysis, particularly functional imaging, is the

need to meaningfully combine results from a subject pool and deducing group

differences. A representation of the observed data for each subject in a common space is

typically required to perform such analysis. Currently, the most widespread approach

used in functional imaging is to spatially normalize the images of subject brains to a

common template or atlas. The availability of easy to use software tools (e.g. The SPM

toolbox [13]) tends to encourage the indiscriminant use of such an approach without due

diligence to the validity of the underlying assumptions involved. Several shortcomings of

this approach have been highlighted in recent studies; the major concern is the validity of

normalization for pathological brains [7-10]. The core idea behind these normalization

approaches, the voxel based morphometry method (VBM) was initially criticized for its

susceptibility to misregistration [11], and this was later corroborated with evidence from

functional studies [14, 15]. These limitations intensified the interest in alternative

methods to analyze the data directly in the subject space without introducing errors due to

the normalization process. Researchers have adopted simple measures of observed data

such as percentage of activation, mean value etc. within specific region of interests

(ROIs) to perform their analysis [16, 17]. While these methods have the advantage of

being simple to compute, they clearly do not incorporate any spatial information of

activation within the ROIs. More recent studies proposed a feature based approach to

characterize and discriminate functional data based on spatial activation patterns [18, 19].

However, these approaches lacked a definite means to account for the structural

variations in the ROI masks. 2

The primary aim of this thesis was to develop a feature based approach to sensitively

discriminate functional patterns of activation in specific regions of interests despite

structural intersubject variations. First, in order to characterize the structural variations,

we developed a spherical harmonics based feature representation for binary ROI masks.

This, in itself, is a significant contribution to ROI shape analysis area since it enabled

direct comparisons of the shape across subjects without a need for mutual registration.

We then extended our feature representation to functional data in order to obtain an

invariant feature representation of the actual spatial distribution of activation within

ROIs. Furthermore, to reduce the effect of structural variations of the ROI shape on these

features, we developed a principal component subspace projection technique that further

increased our method’s sensitivity.

1.2 Principles of Magnetic Resonance Imaging (MRI)

Magnetic resonance imaging was originally referred to as Nuclear Magnetic Resonance

(NMR), based on the underlying physical phenomenon used in image capture and

generation. The core of the technology relies on the fact that protons (nuclear particles)

have a spin, and since protons also carry a positive charge, this results in a magnetic

moment [20]. The net effect of this magnetic moment depends on the number of protons

and neutrons in a nucleus, implying that different elements would have different magnetic

properties. An even number of particles with spin can cancel each other out, thereby

showing no outward manifestation of this effect. However, the nuclei of certain isotopes

of elements like Hydrogen have unpaired particles, thus possessing a net spin. The

average Hydrogen content in the human body is known to be around 63% by mass [21].

3

This makes it an ideal target to manipulate using external magnetic fields to image the

human body.

A nucleus with a net magnetic moment, when placed in a magnetic field of strength B,

will tend to align itself along or opposite to the field direction. Alignment along field

lines is called the low energy state and alignment in the opposite direction is termed the

high energy state. According to the laws of nuclear physics, a particle can switch states

by either absorbing or emitting a photon with energy E equal to the difference between

these two states (1.1) where h is Planck’s constant (h = 6.626x10 -34 J s). This process of

absorption and emission enables the MR phenomenon to be indirectly observed.

(1.1)

γ is called the gyromagnetic ratio, an intrinsic property. The frequency of this photon is

given by (1.2), termed the Larmor frequency.

(1.2)

Consider an object with thousands of such nucleus, the resonance in MRI comes from the

fact that there is continuous exchange of energy between the two states of the nuclear

particles constituting the object. This phenomenon is also termed spin-spin interaction. In

normal conditions, random alignments of particles cancel out and result in a zero net

magnetic moment. However, under the influence of a constant external field B, the

number of particles in the lower energy state (parallel to the field lines) will outnumber

the ones in the higher state (anti-parallel) thereby resulting in the object possessing a net

magnetic moment M0 along a direction parallel to B. According to accepted convention, 4

the static field B is defined to be along the Z direction in 3D Cartesian coordinate system,

BZ. Hence, under equilibrium, the net magnetic moment is given by (1.3)

(1.3)

This equilibrium state can be disrupted by the application of external energy. Depending

on the energy difference between the two states (1.1) for each particle, this would cause

particles to flip and hence change the direction of the net magnetic moment vector. This

external source of energy is usually in the form of a radio frequency (RF) pulse, whose

precise energy is carefully computed to flip the net magnetic moment by a known

amount. Since the energy is pulsed, this flip is temporary, and the particles return back to

the equilibrium state by dissipating energy to their surroundings. According to

terminology from initial applications of MR to study crystal structures, this interaction is

termed spin-lattice interaction. Depending on the energy of the pulse and intrinsic

characteristics of the particles, there is a certain time constant involved before

equilibrium in the direction of magnetic moment is achieved. The time constant, also

called the T1 relaxation time, is defined as the time taken for the magnetic field MZ to

return to 63% of its equilibrium value M0 (1.4)

5

(1.4)

The flipped magnetic moment, also termed the transverse magnetic moment, actually

rotates around the Z axis. Initially, when the external energy is applied, most particles

rotate in phase. After this external source is removed, individual particles being to rotate

differently based on their surroundings. In addition to returning back to equilibrium state

in the direction of magnetism, the rotation also begins to go out of phase. Usually, before

M0 is restored, the rotation settles down from a focused, in phase rotation, to the initial

random phase. The time constant involved in this relaxation of phase is termed T2.

Ideally, the main static field B is assumed to be uniform throughout the substance being

studied, however, in reality the field is not perfectly homogenous. This results in different

parts of the object having different energy differences (1.1), and hence different Larmor

frequencies (1.2), the final result is that the relaxation time T2 is in practice influenced by

both particle interaction and field inhomogeneity resulting in a shorter relaxation time

termed T2*. The T2 time constant can still be measured using repeated complex RF pulse

sequences. Since the magnetic moments are rotating about the Z axis, the magnitude of

moments can be estimated using pick up coils placed in close vicinity. The induced

current in this coil is then observed to deduce the various relaxation times.

6

To obtain an internal image of the substance being studied, the static field B is augmented

with additional fields called the gradient fields. First, a gradient field GZ is applied along

the Z direction. This changes the perceived B value and correspondingly changes the

Larmor frequency (1.1) along the Z axis. Now an RF pulse with energy equal to the exact

Larmor frequency at a given location on the Z axis is applied. Magnetic moment of

particles along the X-Y plane at that location would be selectively flipped by this pulse.

This process is called slice selection since only a thin slice of the object being imaged has

been excited. To further isolate signals picked by the coils to specific (x, y) locations

within this slice, two more gradient fields are used as shown in Figure 1.1.

These gradient fields introduce a controlled phase shift in the precession process of the

spinning particles. The frequency and phase are both reflected in the current signals

picked by the coils. These signals are said to be in K-space since they reflect the

frequency component observed. A Fourier synthesis from this space yields the 2D image

of the slice being studied. This process is then repeated along the volume to obtain a 3D

representation. This is one of the most basic approaches to obtain an MR volume, more

complex pulse sequences, like the echo-planar imaging (EPI) [22] are used in practice.

7

Figure 1.1 Gradient fields along the X and Y axes.

8

1.3 Structural Brain MRI

Various combinations of pulse sequences and measured signals result in a wide array of

possible MR imaging protocols [23]. Currently, the most widespread set of protocols are

those which image the structure of the brain [24]. Structural MRI aims to obtain high

resolution images of the different types of brain tissues. Brain tissue is mainly classified

into:

Grey Matter: Mainly consists of unmyelinated neurons (Myelin is a protective sheath

around axons of the neurons). Grey matter concentration has been known to be

positively correlated with human intelligence.

White Matter: Mainly consists of myelinated neurons. Known to be involved in

message transfer across the human central nervous system

Cerebrospinal fluid (CSF): A clear isotonic fluid which occupies the space inside and

around the human brain. Mainly concentrated in the brain ventricles.

Structural MRI plays a significant role in the diagnosis of neurological diseases like

Multiple Sclerosis [25, 26]; where specific pathological conditions like lesions appear in

the white matter. The high level of detail in imaged brain anatomy enables neuroscientists

to selectively study the anatomy of individual brain structures such as the thalamus,

ventricles etc [2, 3, 27, 28]. The most commonly used brain structure imaging protocols

are the T1 and T2 weighted images (Figure 1.2). Table 1.1 shows the relaxation times for

some of the brain tissue.

9

Table 1.1 MR relaxation times for commonly occurring brain tissue

Tissue Type T1 relaxation time (ms) T2 relaxation time (ms)

Adipose tissue (fat) 240-250 60-80

Cerebrospinal fluid 2200-2400 500-1400

White matter 780 90

Grey matter 920 100

The difference in relaxation times for different tissues shows up as difference in

intensities in the obtained MR image. As the values in the table show, T1 images have a

higher contrast between the various tissues and are more suited for segmentation of brain

tissue. However, certain pathological tissues, like grey matter in multiple sclerosis

affected brain [29], are better contrasted in T2 weighted images. Moreover, as explained

later, T2 images have certain properties that make them sensitive to the amount of oxygen

in the blood, a basic concept used in functional imaging.

Figure 1.2 Whole brain images obtained using different relaxation time weighted protocols showing the different tissue contrasts. Left: T1 weighted image. Right: T2

weighted image.

10

1.3.1 Summary of Structural Data Acquired

The structural data used in this thesis was obtained from MRI scans of 21 control

(normal) subjects and 21 PD patients. Two T1 weighted high-resolution anatomical

images (voxel dimensions 1.0×1.0×1.0mm, 176×256 voxels, 160 slices) were obtained

with a gap of two hours between the two scans. This second observation helps to check

the consistency of our analysis methods. The MR data were acquired on a 3.0 Tesla

Siemens scanner (Siemens, Erlangen, Germany) with a birdcage type standard quadrature

head coil and an advanced nuclear magnetic resonance echoplanar system. Foam padding

was used to limit head motion within the coil.

1.3.2 MR Image Preprocessing

The raw images obtained by MRI are influenced by a variety of noise sources [30]. Basic

preprocessing steps are necessary to increase the SNR, most importantly when automated

analysis of the images follows. The pre-processing stage typically involves a varying

number of steps depending on the nature of the study; here we explain the steps carried

out in processing our data within the context of the work presented in this thesis.

1.3.2.1 Brain Extraction

MR images of the brain normally include signal from the brain tissues, spinal chord, eyes,

nasal cavity etc. These regions are typically not of interest and need to be excluded from

the image data that is to be analyzed, moreover regions like the nasal cavity actually

degrade MR signal around it. The presence of these artifacts is seen as a confounding

factor for most automatic registration methods, typically employed in multi-subject

studies, hence the importance of skull stripping or brain extraction [31][32].

11

Figure 1.3 Left: A raw T1 weighted image (axial slice), notice the noise near the nasal cavity and the eyes (upper part of image). Right: The extracted brain using the combined expectation maximization and geodesic active contour method proposed by Huang et al

[33].

To process the data in this thesis, we use a recently proposed fully automated method by

Huang et al [33] which was shown to provide quantitative advantages over existing

methods. This technique begins by first pre-processing MRI scans to generate inputs to a

deformable model – a geodesic active contour [70]. After the model converges to a stable

solution, the mask is post-processed to further refine the perimeter of the brain cortex.

The pre-processing and post-processing stages employ the expectation-maximization

(EM) algorithm on a mixture of Gaussian models as well as mathematical morphology

and connected component analysis. Figure 1.3 shows the result of using this technique on

one of our subject’s T1 weighted brain MR volume.

1.3.2.2 Anisotropic Diffusion Filtering

Most brain tissue and shape analysis techniques are automated and require a high SNR

for effective results. One of the most common preprocessing steps is in reducing the

impact of noise using spatial smoothing. Normal Gaussian kernel based spatial filters are

12

not well suited for smoothing structural MR data since the isotropic nature of the kernels

would affect the signal integrity near tissue boundaries. As explained later, these

boundaries guide automated segmentation of brain tissues and regions and thus need to be

preserved. A form of antistrophic smoothing proposed by Perona et al [34] is widely used

in MR image processing to preserve the edges while improving the SNR. Anisotropic

filters have spatially varying diffusion coefficients which allow them to selectively

perform intra-region smoothing rather than inter-region smoothing, thereby reducing the

degradation of image boundaries. We used an ITK [35] implementation of a 3D version

of this popular filter to process our structural data. Figure 1.4 shows the effect of using

this filter on a noisy T1 brain image.

Figure 1.4 Result of anisotropic diffusion filtering on a T1 brain volume (one slice shown).

13

1.3.3 Segmentation of Regions of Interest in the Brain

Segmentation of brain areas involves the process of localizing specific regions within the

brain, either based on tissue class or based on the constituting brain structure.

Segmentation methods can be broadly classified into manual, semi-automatic and

automatic segmentation techniques [36, 37]. Accurate segmentation of specific regions

in the brain is very important for region of interest (ROI) based analysis approaches. In

the study of shape or structure of brain regions like the thalamus for example, errors in

segmentation can have a very significant impact on the analysis and subsequent medical

inference. ROI segmentations are almost always done on high resolution anatomical

scans, like the T1 MR volumes. As explained in later sections, functional studies, which

involve comparatively lower resolution scans make provision to acquire a high resolution

anatomical (usually T1) volume to enable segmentation of regions of interest.

1.3.3.1 Manual Segmentation of the Thalamus

Most of the ROIs obtained for the data used in this thesis were segmented using manual

techniques. Considerable experience is required to identify and delineate some of the

ROIs in MR images (Figure 1.13). Even though this is a very time consuming process,

manual segmentation by a trained expert is considered a gold standard in segmentation

applications. A number of software packages exist to help trained neuroscientists

accurately delineate regions of the brain in MR images. ROIs involved in the functional

study (explained in section 1.4) were segmented manually using the Amira software

package (Mercury Computer Systems, San Diego, USA) on the collected T1 images. Two

of these ROIs, the left and the right thalamus were selected for structural analysis since it

was shown that they undergo atrophy in Parkinson’s disease patients [38].14

1.3.3.2 Automatic Segmentation of Brain Ventricles

Manual segmentation processes are frequently limited by the availability of trained

experts and the time involved in the process. Automatic segmentation methods are

preferred whenever the region of interest has a high SNR and when its accuracy and

robustness have been thoroughly tested. We used the voxel based morphometry (VBM)

[39] approach to segment the left and right brain ventricles from the T1 brain volume

scans. Despite its known limitation in aligning cortical features of the brain [11], it was

expected to perform better for the ventricles due to their high-contrast and relatively more

regular boundaries compared to the cortical gyri and sulci [40]. First, the left and the right

ventricles were individually segmented on the tissue probability map (TPM) for the

cerebrospinal fluid (CSF), then, using the VBM normalization approach, these maps were

warped on to the subject brain. The areas in the subject brain corresponding to the

segmented area on the TPM were labeled as the ventricles. A connected component

analysis was then used to clean out the segmented ventricle of small disconnected voxels.

Figure 1.5 displays the result of one such segmentation.

15

Figure 1.5 Result of the automatic segmentation of the right brain ventricle. The left ventricle’s binary ROI mask is rendered on orthogonal slices of the subjects T1 image.

1.3.4 Quantifying Structural Changes in Brain ROIs

It is now well known that the brain consists of different regions each associated with

different functionality. It is also known that some neurological diseases affect certain

parts of the brain; this has encouraged targeted analysis of anatomical regions in the hope

of learning more about these diseases [5, 27, 28]. A region of interest (ROI) is a specific

part of the brain delineated in 3D space either using automatic segmentation or manual

methods for such a targeted study. While analyzing the structural features of an ROI, the

data being analyzed is the binary ROI mask of the region in question.

The simplest and most common approach to quantify the binary ROI mask is to use the

volume or the voxel count (number of voxels contained in the ROI), e.g. Anstey et al

used the hippocampal volume to investigate changes observed in mild cognitive

impairment (MCI) [41]. However, studies using volumetric measures do not reflect shape

changes that might be indicative of neurological change. Vetsa et al. used medial

16

representations to characterize the surface of the caudate and identify shape changes in

schizophrenia [42]. This approach requires accurate alignment of the ROIs across

different subjects for valid analysis and hence residual errors in mutual alignment could

adversely affect the final results.

Alternate methods to quantify this mask rely on obtaining descriptive feature vectors

which reflect the structural information in an ROI. These features may be invariant to

rotations, translations and scale, thus enabling easy comparison across different subjects.

This eliminates the need for mutual alignment, saving time and potential inconsistencies

arising from registration errors. Zimring et al [43] used spherical harmonic (SPHARM)

based invariant indices to accurately estimate and study volume of brain lesions, reducing

the errors due to subject positioning. Tootoonian et al [28] used scale, rotation and

translation invariant features derived using a SPHARM representation of 3D ROIs to

analyze shape changes in brain MRI data and demonstrated the advantages of using such

an approach along with traditional volumetric analysis. However, the parameterization

technique used there did not allow for shapes with non-convex topology. Gerig et al [44]

proposed using a SPHARM surface representation for brain structures like the ventricles

to better understand neurodevelopment and neurodegenerative changes. Their approach

however requires explicit alignment of the structures along with volume normalization

and is valid only for structures with spherical topology.

1.3.4.1 SPHARM features for Quantifying Structure in Brain ROIs

This thesis presents a novel way to quantify 3D ROIs obtained from brain MR images

using invariant spherical harmonics based features. Unlike previous implementations

17

[68,69], this approach places no restriction on the allowable topology of the ROI masks

while ensuring that the obtained features are unique to its shape. These features are

translation, scale and rotational invariant which allow them to be directly compared

between subject groups without a need for mutual registration. The sensitivity of these

features was validated on synthetic data with realistic intersubject variability.

Furthermore, application of this method to the ROI masks of the left and right thalami of

real PD patient data revealed systematic difference in shape when compared to normal

subjects [27]. Section 2 describes the method in detail including derivations and synthetic

tests along with preliminary clinical results. Section 3 and Section 4 build on the results

and presents the clinical relevance of our findings.

1.4 Functional Magnetic Resonance Imaging

Functional magnetic resonance imaging (fMRI) is currently one of the most actively

researched branches of the MR technique. Using MR pulse sequences which can detect

change in the blood Oxygen content, this imaging modality can be used to localize

regions in the brain responding to specific stimuli. Neuroscientists use this technique on

normal human subjects to obtain functional maps of the brain describing the role of

various regions in processing common cognitive tasks. These maps enable them to

compare the functional responses of pathological brains, enabling a detailed study of the

effects of neurological damage on functional response. Recently, using this technique,

researchers have been able to show plastic reorganization of neurocognitive networks

which would otherwise not be detected using outward manifestation of symptoms [12,

45].

18

1.4.1 Principles of BOLD imaging

The seminal work by Ogawa et al [46] laid the foundation for the study of function using

MR imaging. It was noticed that oxygenated and deoxygenated blood have distinct T2

relaxation times due to their different magnetic properties (Table 1.2). In practice, due to

magnetic field in-homogeneities, the observed relaxation time is much faster and is called

the T2* signal.

Table 1.2 MR relaxation time for Oxygenated and Deoxygenated blood

Blood Type T1 relaxation time (ms) T2 relaxation time (ms)

Oxygenated blood 1350 50

Deoxygenated blood 1350 200

This phenomenon, however, does not enable precise computation of the amount of

Oxygen in the blood. Instead, neuroscientists use this to measure the change in blood

Oxygen concentrations, hence the name blood oxygen level dependent (BOLD) imaging.

1.4.2 Hemodynamic Response

The change in blood Oxygen content in response to activation in neurons is called the

Hemodynamic response. Neurons are the computing cells of the brain, a basic unit which

processes the various stimuli that the brain receives. In response to a specific stimulus, 19

neurons associated with the region that processes this information are activated. Active

neurons require energy derived from bio-chemical reactions which consume Oxygen.

Hence an increase in activation levels requires a larger amount of Oxygen when

compared to the rest state. This increase in Oxygen requirement triggers a Hemodynamic

response which increases the blood flow into these regions. However, this process

overcompensates and results in an increased oxygenated blood flow into the active

regions [47]. From an imaging point of view, if this region was monitored before the

stimulus was presented and after the Hemodynamic response was triggered, a change in

the T2* signal would be observed. In practice, this change is of a very small magnitude

and hence hard to detect. Neuroscientists resort to the basic technique of obtaining

repeated observations to obtain a better SNR. A comprehensive review by Heeger et al

outlines this process is more detail [48].

1.4.3 Functional Experiment Setup

The main challenge in functional imaging is to overcome the low SNR observed in the

BOLD signal. Given the current limitations of MR scanners in terms of image resolution,

SNR and the acquisition time, the most robust fMRI experiment used is the block design

approach. This is also the simplest and easy to analyze technique unlike other more

complex schemes like event based experiments. In the single task block design, a subject

performs a given task repeatedly, in blocks of time (duration), while MR brain images are

being continuously acquired. The tasks are interspersed with rest periods to let the

Hemodynamic response settle down to baseline levels. The data so obtained is also called

the time-series or the 4D functional data. Given this structure of a functional experiment,

the volumes (3D brain images) need to be acquired with the sufficiently small acquisition

20

time to accurately sample the BOLD response. This temporal resolution requirement

limits the spatial resolution of fMRI volumes; often the functional volumes acquired have

a very low spatial resolution compared to the structural images obtained (which have a

longer acquisition time). Usually, a high resolution structural scan is separately obtained

before or after the functional experiment. Functional activations observed in the fMRI

data can then be examined for correspondence to physical structures using the anatomical

scans. ROIs drawn on the anatomical scans can be mapped to the functional data to

enable ROI based analysis of the time series. The precise nature of the applied stimulus

or task performed varies with each fMRI study [49].

1.4.3.1 Bulb Squeezing Task Experiment

In neurological diseases like Parkinson’s disease (PD), one of the primary external

manifestations of the disease is motor task related disabilities. Hence, a motor task

involving the squeezing of a bulb was used in our study. Subjects lay on their back in the

functional magnetic resonance scanner viewing a computer screen via a projection-mirror

system. All subjects used an in-house designed response device in their right hand, a

custom-built MR-compatible rubber squeeze-bulb (Figure 1.6) connected to a pressure

transducer outside the scanner room.

21

Figure 1.6 The MR-compatible rubber squeeze bulb used in the functional experiment

The subjects lay with their forearm resting down in a stable position, and were instructed

to squeeze the bulb using an isometric hand grip and to keep their grip constant

throughout the study. Using the squeeze bulb, subjects were required to control the width

of an “inflatable ring” (shown as a black horizontal bar on the screen) in order to keep the

ring within an undulating pathway without scraping the sides (Figure 1.7).

Figure 1.7 Visual feedback given to subject performing the bulb squeezing task. The width of the black horizontal bar reflected the amount of ‘squeezing’ that the bulb

recorded. Subjects had to modulate the squeezing action to keep the width within the undulating white pathway.

22

The pathway used a block design with sinusoidal sections in two different frequencies

(0.25 and 0.75 Hz) in a pseudo-random order, and straight parts in between where the

subjects had to keep a constant force (Figure 1.8).

Figure 1.8 The stimulus design used for the functional study. The tunnel width shown on the Y axis indicates the width of the undulating pathway shown in Figure 1.7.

The frequencies were chosen based on prior findings and pilot studies were used to

determine that PD subjects could comfortably perform the required task. Each block

lasted 20 seconds, alternating a sinusoid, constant force, sinusoid and so on to a total of 4

minutes. Before the first scanning session, subjects practiced the task at each frequency

until errors stabilized and they were familiar with the task requirements. Custom Matlab

software (The Mathworks, Natick, MA) and the Psychtoolbox [50] were used to design

the stimulus and present the visual feedback.

1.4.4 Summary of Functional Data Acquired

Functional MRI for the experiment described in the section 1.4.3.1 was acquired on a

Philips Achieva 3.0 T scanner (Philips, Best, the Netherlands) equipped with a head-coil.

Echo-planar (EPI) T2* weighted images with blood oxygenation level-dependent (BOLD)

contrast were acquired. The 2D slice acquired had a matrix size of 64 x 64 with pixel size 23

3 x 3 mm. Thirty-six axial slices of 3mm thickness were collected in each volume, with a

gap thickness of 1mm. Slices were selected to cover the dorsal surface of the brain and

include the cerebellum ventrally. A high resolution, 3-dimensional T1-weighted image

consisting of 170 axial slices was also acquired of the whole brain to facilitate anatomical

localization of activation for each subject. Figure 1.9 shows a sample T1 slice against a

time sequence of T2*.

Figure 1.9 Left: A slice from a T1 weighted anatomical scan of a subject. Right: Corresponding slices of T2* scans from functional volumes acquried the duration of the

experiment (130 such volumes were collected over a duration of 260 seconds).

1.4.5 fMRI Data Preprocessing

The raw time course of the fMRI data has to be put through a complex image processing

pipeline before the final results can be obtained. The following is a brief introduction to

the various steps in this pipeline. While it includes most of the commonly used steps, it

must be noted that there is considerable variation in the methods themselves and the order

in which they are used [51]. Most fMRI studies collect the functional time-series as well

as at least one high resolution anatomical image. The task performed and the image

24

acquisition parameters are assumed to be the same for all subjects involved. While some

studies are limited to a single subject, especially in cases of rare neurological conditions,

most studies image a number of subjects. These subjects are usually age and sex matched

between two different populations under study (for example, PD patients and normal

subjects). The goal of the analysis then is to use the data from individual subjects and

deduce the global group-wise difference in activation response.

1.4.5.1 Brain Extraction and Co-registration

The first step is similar to the preprocessing involved in structural scans (Section 1.3.2.1).

The brain is extracted from the raw MR image individually. The structural scan is then

aligned to the first volume of the functional time series to compensate for any subject

movement between the two scans. This registration is rigid; involving translation and

rotation about the three axes. This process helps neuroscientists to identify regions in the

brain which would otherwise have been difficult using the low spatial resolution fMRI

images.

Figure 1.10 The process of brain extraction, followed be co-registration of the high resolution T1 anatomical scan to the first functional T2* voume

25

1.4.5.2 Slice Timing Correction for Individual Functional Volumes

As explained earlier, the 3D volume acquisition of the brain proceeds with the sequential

acquisition of single 2D slices. This implies that each slice of a volume is acquired with a

definite time lag with respect to the previous slice. Slice timing correction is important in

functional analysis since slice acquisition differences appear as a phase shift in the time-

series of individual voxels. Since the BOLD signal being analyzed is temporal in nature,

this artifact can confound further analysis. Slice timing correction procedures attempts to

correct for this time difference by correcting the phase of each acquired slice in the

Fourier domain without affecting the magnitude of the observed signal. Slice timing

correction was applied using Sinc interpolation in Brain Voyager (Brain Innovations, the

Netherlands, www.brainvoyager.com) for the data collected for analysis in this thesis.

1.4.5.3 Motion Correction of Functional Volumes

A complete fMRI study scan requires the subject to be inside the MRI scanner for up to

an hour depending on the experiment design. Despite head rests and motion arrestors in

the machine, it is inevitable that there is some amount of displacement in the subject’s

position during the course of the scan. Since the fMRI data analysis depends on the time

series analysis of a voxel, there is an inherent assumption that a specific voxel always

corresponds to the same physical volume throughout the session. Head motion correction

steps attempt to rectify this situation by realigning individual scans.

Typically, in cases of stronger forms of stimuli, subjects tend to move in synch with the

change in stimulus (stimulus correlated motion) [52]. This causes a periodic change in the

time course of a voxel which is in phase with the stimulus. These types of artifacts will

26

have an adverse effect on the analysis and may as well render the entire data unfit for

analysis. Researchers usually analyze the data sets manually and screen out data sets

which show large head motions.

A common practice is to align all the functional volumes to the first acquired volume.

This is achieved using rigid registration processes, usually based on the intensity metric

[53]. Accurate motion correction is extremely important, since task correlated head

motion (common in motor tasks) can have adverse influence on the functional analysis.

There a number of practical approaches to correct for subject motion [54]. The data used

in this thesis was processed with a motion corrected independent component analysis

(MCICA) method proposed by Liao et al [55].

Figure 1.11 Motion correction re-aligns the functional volumes in case the subject moves during the time course of acquisition.

1.4.5.4 3D Spatial Smoothing of the Functional Volumes

Spatial smoothing involves using a 3D kernel to remove high frequency component in the

individual fMRI volumes [56]. Spatial smoothing is primarily done to increase the SNR.

Smoothing is also assumed to reduce the effect of any residual error in the motion

27

correction and registration process, by increasing the effective overlap between assumed

homologous regions across subject brains. One branch of fMRI analysis also requires an

estimate of the smoothness in the data for multiple comparison correction [57]. Often,

since the true smoothness cannot be estimated, it is taken to be equal to the amount of

smoothing performed. Given that fMRI resolution is low to begin with, smoothing can

lead to signal degradation and reduced sensitivity in later analysis steps [58, 59].

The functional data used in this thesis was not smoothed to enable the derived features to

be more sensitive to spatial locations of activation statistics. The feature based

characterization approach described in this thesis does not require an estimate of

smoothness of the data; neither does it employ registration to warp the functional data.

Moreover, the sensitivity of the proposed features despite high SNR further validates

using the functional data as is, without any smoothing.

1.4.6 Functional Activation Map Generation for Individual Subjects

The first post-processing step in fMRI analysis is to individually analyze a subject’s

functional response. The goal of this step is to obtain a measure of activation in each

voxel of the subject’s brain. There are numerous methods to obtain this measure, with a

common approach being to study the time course of each voxel and compare it against an

expected response in order to obtain a parametric measure of confidence in their

similarity. A major hurdle is in defining the expected response. One of the most simple

and widely used methods is to model the Hemodynamic response as a Volterra kernel

[60] function and convolve this with a boxcar function representing the task-rest periods.

Various approaches are then defined to obtain an activation metric ranging from simple

28

correlation [61] to general linear models [13]. One drawback of these approaches is in

the assumption that the Hemodynamic response is uniform in time and space.

In this thesis, we use a more sophisticated approach based on independent component

analysis (ICA) to extract the components involved in the observed time course.

McKeown et al [62] showed that this approach could efficiently describe the response

and isolate effects of non-task related signals, movements and other artifacts. The end

result of a subject level analysis is what is called a statistical parameter map (SPM). This

SPM is a 3D volume with the value at each voxel position representing a quantitative

measure of confidence of that location being active during the task.

Figure 1.12 The process of obtaining subject level statistical parameter maps. The time course of each voxel is statistically compared to an expected response based on the task

performed to obtain a parameter which describes the activation at that voxel. This process is repeated for all voxels in the brain resulting in the subject level SPM.

29

1.4.7 Differences in Activation Maps at the Group Level

Once the subject level parameter maps have been obtained, the next step in functional

analysis is to combine maps within each group and compare them against each other.

This is a key step in functional analysis and there has been quite a few competing

methods proposed. A main contribution of the thesis is in this step of functional analysis.

By far the most popular approach is to warp each subject’s brain to a common atlas,

thereby spatially normalizing it [63]. Then the difference in means of the parameter at

each voxel location between the two groups is statistically tested for significant

difference. A final group level parameter map is then generated using the results of this

statistical analysis. Further inferences are drawn directly from this map. This approach

heavily relies on the non-rigid registration processes to perform the warping of the brain.

A comparison of some of these methods was presented by Crivello et al. [64]. However,

given the large amount of intersubject variations in the human brain, current spatial

normalization methods may give an imperfect registration result [14]. This might result in

signals from functionally distinct areas, especially small subcortical structures, to be

inappropriately combined [15]. Spatial normalization may therefore lead to poor

sensitivity in the fMRI data analysis due to reduced functional overlap across subjects, as

observed by Stark and Okado [65].

An alternative approach more recently investigated is to align the subjects at the region of

interest (ROI) level, as opposed to whole brain normalization. These studies are usually

hypothesis driven and examine signals from specific parts of the brain. Miller et al. [66]

extended the work of Stark and Okado [65] by utilizing large deformation diffeomorphic

30

metric mappings (LDDMM). Also, an approach that uses continuous medial

representations (cm-rep) of the ROIs has been proposed [67]. However, these approaches

rely on structural features and manually placed landmarks in the higher resolution scans

to deform the functional maps into a common space.

To circumvent these potential problems associated with normalization, many researchers

employ feature based ROI analysis without using any normalization [16]. This results in

enhanced sensitivity in activation detection in some cases [17]. However, to date, most

methods ignore information encoded by the spatial distribution of the activation statistics

and instead use simpler invariant (to pose) measures such as mean voxel statistics or

percentage of active voxels within an ROI as features [16].

An attempt in incorporating spatial information was proposed in [19] using sums of

activation statistics within spheres of increasing radii. However, these features have

limited sensitivity to spatial patterns since they only capture changes in the radial

direction. Ng et al. [18] proposed an alternate approach employing three dimensional

moment invariant features (3DMI) which were shown to be more sensitive than

conventional mean voxel statistics and percentage of activated voxels based approaches

in detecting task-related activation differences. While a novel and interesting approach by

itself, the method does not account for intersubject variability present in the ROI masks

or its effect on the analysis. Also, as the authors note, higher order 3DMI features are

more susceptible to noise and hence limit the maximum number of discriminative

features that can be derived [18].

31

SPHARM-based methods have previously been proposed in the context of 3D shape

retrieval systems by Vranic et al [68] and Kazhdan et al [69]. Both authors proposed

obtaining invariant SPHARM features by intersecting 3D shapes with shells of growing

radii. This approach, however, could not detect independent rotations of a shape along the

shells, thereby resulting in a non-unique representation [69]. In [28], the use of invariant

SPHARM descriptors for analyzing anatomical structures (represented as binary 3D

shapes) in MR was proposed. However, the shape parameterization employed was limited

to convex topologies, which significantly limits its applicability. The three approaches

described above were used to analyze the geometrical shape of an ROI surface, not the

intensity distributions of an ROI volume, such as the spatial activation patterns in fMRI

data.

1.4.7.1 SPHARM Features for Analyzing Spatial Activation Patterns

This thesis proposes the use of SPHARM features to characterize spatial patterns of

activation in functional MR data for the first time. These features are invariant to scale,

translation and rotation and hence can be directly compared across subjects, thus avoiding

the various problems associated with the normalization approach. The affect of

anatomical variability between subjects on these functional features is accounted for by

using a novel principal component subspace approach. Synthetic data experiments

constructed with real brain ROIs and synthetically created spatial activation patterns

showed significantly improved performance of the SPHARM approach against one of the

latest spatial normalization approaches. Furthermore, when applied to real data,

SPHARM features were able to detect changes in regions which were unnoticed using the

32

conventional normalization approach. Some of the ROIs analyzed in the real data set are

shown in Figure 1.13.

Figure 1.13 The functional ROIs studied in this thesis. All ROIs shown occur in pairs (in the left and righ brain hemishpheres), only regions in left hemisphere are shown.

Indicated ROIs are Prefrontal cortex (PMC), Supplementary motor cortex (SMA), Primary motor cortex (M1), Caudate (CAU), Putamen (PUT), Thalamus (THA),

Cerebellar hemisphere (CER).

1.5 Thesis Contributions

This thesis makes three important contributions to region based analysis of MR images.

The first contribution enables generating invariant SPHARM features to describe 3D

functions uniquely. The second contribution involved extending this method to analyze

spatial patterns of activation in functional data. Finally, the principal component subspace

approach presented reduces the impact of anatomical variations in the functional features.

33

1.5.1 Structural ROI Analysis

An automated feature based discrimination method which complements traditional

volumetric analysis of anatomical ROIs using structural features was presented. These

SPHARM features are invariant to translation, rotation and scale, thereby eliminating the

need for mutual registration or spatial normalization as required by other methods.

Moreover, unlike other methods, there is no need for manual intervention once the ROIs

are obtained. This reduces any chance of bias or variability in landmark placement which

might affect the results of mutual registration dependent methods.

This approach was used to analyze real data and was able to discriminate shape changes

in the thalami [27] and ventricles of PD patients. Group representation using shapes

closest to group-mean vectors enabled neuroscientists to further study the nature of the

change observed. With increasingly accurate and robust automatic segmentation

algorithms being developed, this feature based approach has the potential to be

completely automated once the raw MRI image is obtained.

In summary, the contributions of this thesis to ROI based shape analysis are:

Addressed previous limitations of SPHARM based invariant feature

representation using a radial transform to obtain unique features, thereby

extending its use to more complex shapes including those with possible spatial

disconnects.

Use of this SPHARM based unique invariant features for the analysis of shape in

anatomical regions of interest.

34

1.5.2 Functional ROI Analysis

Spatial patterns of activation have been shown to be more sensitive than traditional mean

or percentage activation in the analysis of fMRI data [18]. In this thesis we presented a

novel scheme to quantify and analyze spatial functional patterns using SPHARM

features. For the first time, we proposed the use of a principal component subspace

approach to quantify and reduce the influence of intersubject anatomical variability in

functional pattern analysis using feature based representation. Using projections on this

reduced subspace we demonstrated improved sensitivity by minimizing confounding

effects of inter-subject anatomical variations seen in ROI binary masks. A significant

improvement over a recently proposed ROI normalization approach was shown using

synthetic data with real world intersubject anatomical variability modeled. The proposed

method was then applied to real fMRI data collected from PD patients and normal

subjects. In addition to the ROIs detected by the normalization approach, SPHARM

features detected changes in activation pattern of clinically relevant ROIs.

In summary, for the analysis of functional activation patterns in regions of interest in

fMRI data, the contributions of this thesis are:

Invariant SPHARM based feature representation for ROI based fMRI data

analysis

Principal component subspace approach to reduce the impact of intersubject

structural variability in the functional analysis

35

1.6 Thesis Overview

Sections in this thesis are based on the following manuscripts:

Section 2: Invariant SPHARM features for anatomical ROIs are introduced.

Contributions in addressing previous limitations are presented along with a clinical

application for shape analysis of the thalamus in PD patients.

o Ashish Uthama, Rafeef Abugharbieh, Anthony Traboulsee and Martin J.

McKeown , "Invariant SPHARM shape descriptors for complex geometry MR

region of interest analysis in MR region of interest analysis," Engineering in

Medicine and Biology, pp. 1322-1325, 2007.

Section 3: Clinical relevance of the SPHARM features are presented with shape

changes observed in the PD thalamus discussed in greater detail.

o Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer,

Mechelle Lewis and Xuemei Huang, “Shape (But Not Volume) Changes in

the Thalami in Parkinson Disease”, Submitted to BioMed Central

Neuroscience, 2007.

o Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer,

Mechelle Lewis and Xuemei Huang, "MRI in Parkinson's Disease identifies

shape, but not volume changes in the thalamus", Abstract, Selected for poster

presentation at XVII WFN World Congress on Parkinson's Disease and

Related Disorders, Amsterdam, The Netherlands, 2007

36

Section 4: Invariant SPHARM shape features were applied to the study of shape

change in lateral brain ventricles in PD patients.

o Ashish Uthama, Rafeef Abugharbieh and Martin J. McKeown, "Invariant

SPHARM shape descriptors for the analysis of brain ventricles", manuscript

being prepared for submission.

Section 5: SPHARM features are extended to characterize 3D spatial activation

patterns in functional MR imaging. A novel principal component subspace approach

to reduce influence of anatomical variability is presented.

o Ashish Uthama, Rafeef Abugharbieh, Anthony Traboulsee, Martin J.

McKeown, “3D Regional fMRI Activation Analysis Using SPHARM-Based

Invariant Spatial Features and Intersubject Anatomical Variability

Minimization”, manuscript being prepared for submission.

Section 6: Functional MR SPHARM features are compared against a competing,

state-of-art normalization approach.

o Ashish Uthama, Rafeef Abugharbieh, Martin J. McKeown, Samantha J.

Palmer, Anthony Traboulsee and Martin J. McKeown, “Characterizing fMRI

Activations in ROIs while Minimizing Effects of Intersubject Anatomical

Variability”, manuscript being prepared for submission.

Section 7: Conclusion and future work.

37

1.7 References

[1] D. Mamah, L. Wang, D. Barch, G. A. de Erausquin, M. Gado and J. G. Csernansky,

"Structural analysis of the basal ganglia in schizophrenia," Schizophrenia. Research, vol.

89, pp. 59-71, 2007.

[2] D. Jang, J. Kim, T. Chung, S. K. An, Y. C. Jung, J. Lee, J. Lee, I. Kim and S. I. Kim,

"Shape deformation of the insula in schizophrenia,” Neuroimage, vol. 32, pp. 220-227,

2006.

[3] J. J. Levitt, C. F. Westin, P. G. Nestor, R. S. Estepar, C. C. Dickey, M. M. Voglmaier,

L. J. Seidman, R. Kikinis, F. A. Jolesz, R. W. McCarley and M. E. Shenton, "Shape of

caudate nucleus and its cognitive correlates in neuroleptic-naive schizotypal personality

disorder," Biological Psychiatry, vol. 55, pp. 177-184, 2004.

[4] L. Shen, "A surface-based approach for classification of 3D neuroanatomic

structures,” Intelligent Data Analysis, vol. 8, pp. 519-542, 2004.

[5] M. Styner, J. A. Lieberman, D. Pantazis and G. Gerig, "Boundary and medial shape

analysis of the hippocampus in schizophrenia," Medical Image Analysis, vol. 8, pp. 197–

203, 2004.

[6] Bermel. Selective caudate atrophy in multiple sclerosis: A 3D MRI parcellation study.

Neuroreport 14(3), pp. 335, 2003

38

[7] S. Krishnan, M. J. Slavin, T. T. Tran, P. M. Doraiswamy and J. R. Petrella, "Accuracy

of spatial normalization of the hippocampus: implications for fMRI research in memory

disorders," Neuroimage, vol. 31, pp. 560-571, 2006.

[8] H. Juch, I. Zimine, M. Seghier, F. Lazeyras and J. D. Fasel, "Anatomical variability of

the lateral frontal lobe surface: implication for intersubject variability in language

neuroimaging," NeuroImage, vol. 24, pp. 504-514, 2005.

[9] M. W. G. Vandenbroucke, R. Goekoop, E. J. J. Duschek, J. C. Netelenbos, J. P. A.

Kuijer, F. Barkhof, P. Scheltens and S. A. R. B. Rombouts, "Interindividual differences

of medial temporal lobe activation during encoding in an elderly population studied by

fMRI," NeuroImage, vol. 21, pp. 173-180, 2004.

[10] K. Swallow, T. Braver, A. Snyder, N. Speer and J. Zacks, "Reliability of functional

localization using fMRI," NeuroImage, vol. 20, pp. 1561-1577, 2003.

[11] F. L. Bookstein, ""Voxel-based morphometry" should not be used with imperfectly

registered images," Neuroimage, vol. 14, pp. 1454-1462, 2001.

[12] R. Mallol, A. Barrós-Loscertales, M. López, V. Belloch, M. Parcet and C. Ávila,

"Compensatory cortical mechanisms in Parkinson's disease evidenced with fMRI during

the performance of pre-learned sequential movements," Brain Research, vol. 1147, pp.

265-271, 2007.

[13] K. J. Friston, A. P. Holmes, K. J. Worsley, J. B. Poline, C. Frith and R. S. J.

Frackowiak, "Statistical Parametric Maps in Functional Imaging: A General Linear

Approach," Human Brain Mapping, vol. 2, pp. 189-210, 1995.

39

[14] O. T. Carmichael, H. A. Aizenstein, S. W. Davis, J. T. Becker, P. M. Thompson, C.

C. Meltzer and Y. Liu, "Atlas-based hippocampus segmentation in Alzheimer's disease

and mild cognitive impairment," Neuroimage, vol. 27, pp. 979-990, 2005.

[15] M. Ozcan, U. Baumgartner, G. Vucurevic, P. Stoeter and R. Treede, "Spatial

resolution of fMRI in the human parasylvian cortex: Comparison of somatosensory and

auditory activation," Neuroimage, vol. 25, pp. 877-887, 2005.

[16] R. T. Constable, P. Skudlarski, E. Mencl, K. R. Pugh, R. K. Fulbright, C. Lacadie, S.

E. Shaywitz and B. A. Shaywitz, "Quantifying and Comparing Region-of-Interest

Activation Patterns in Functional Brain MR Imaging: Methodology Considerations,"

Magnetic Resonance Imaging, vol. 16, pp. 289-300, 1998.

[17] A. Nieto-Castanon, S. S. Ghosh, J. A. Tourville and F. H. Guenther, "Region of

interest based analysis of functional imaging data," Neuroimage, vol. 19, pp. 1303-1316,

2003.

[18] B. Ng, R. Abugharbieh, X. Huang and M. J. McKeown, "Characterizing fMRI

activations within regions of interest (ROIs) using 3D moment invariants," in Computer

vision and Pattern Recognition Workshop, pp 63, 2006,

[19] D. Kontos and V. Megalooikonomou, "Fast and effective characterization for

classification and similarity searches of 2D and 3D spatial region data," Pattern

Recognition, vol. 38, pp. 1831-1846, 2005.

[20] K. Tanaka, "Basic principles of magnetic resonance imaging," Rinsho Byori, vol.

48, pp. 614-620, 2000.

40

[21] M. A. Foster, Magnetic Resonance in Medicine and Biology. Pergamon Press, 1984.

[22] M. Poustchi-Amin, S. A. Mirowitz, J. J. Brown, R. C. McKinstry and T. Li,

"Principles and applications of echo-planar imaging: a review for the general radiologist,"

Radiographics, vol. 21, pp. 767-779, 2001.

[23] E. F. Jackson, L. E. Ginsberg, D. F. Schomer and N. E. Leeds, "A review of MRI

pulse sequences and techniques in neuroimaging," Surgical Neurology, vol. 47, pp. 185-

199, 1997.

[24] M. Symms, H. R. Jager, K. Schmierer and T. A. Yousry, "A review of structural

magnetic resonance neuroimaging," Journal of Neurology Neurosurgery and Psychiatry.,

vol. 75, pp. 1235-1244, 2004.

[25] A. Traboulsee, "MRI relapses have significant pathologic and clinical implications

in multiple sclerosis,” Journal of Neurological Science, vol. 256 Supplement 1, pp. S19-

22, 2007.

[26] R. Bakshi, "Magnetic resonance imaging advances in multiple sclerosis," Journal of

Neuroimaging, vol. 15, pp. 5S-9S, 2005.

[27] A. Uthama, R. Abhugharbieh, A. Traboulsee and M. J. McKeown, "Invariant

SPHARM shape descriptors for complex geometry MR region of interest analysis in MR

region of interest analysis," Engineering in Medicine and Biology, pp. 1322-1325, 2007

41

[28] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs. volume:

Invariant shape descriptors for 3D region of interest characterization in MRI," in

International Symposium on Biomedical Imaging, pp. 754-757, 2006.

[29] R. Bakshi, R. H. B. Benedict, R. A. Bermel, S. D. Caruthers, S. R. Puli, C. W. Tjoa,

A. J. Fabiano and L. Jacobs, "T2 Hypointensity in the Deep Gray Matter of Patients With

Multiple Sclerosis: A Quantitative Magnetic Resonance Imaging Study," Archives of.

Neurology, vol. 59, pp. 62-68, 2002.

[30] A. Macovski, "Noise in MRI,” Magnetic Resonance Medicine, vol. 36, pp. 494-497,

1996.

[31] K. Boesen, K. Rehm, K. Schaper, S. Stoltzner, R. Woods, E. Luders and D.

Rottenberg, "Quantitative comparison of four brain extraction algorithms," Neuroimage,

vol. 22, pp. 1255-1261, 2004.

[32] J. M. Lee, U. Yoon, S. H. Nam, J. H. Kim, I. Y. Kim and S. I. Kim, "Evaluation of

automated and semi-automated skull-stripping algorithms using similarity index and

segmentation error," Computational and Biological Medicine, vol. 33, pp. 495-507,

2003.

[33] A. Huang, R. Abugharbieh, R. Tam and A. Traboulsee, "MRI Brain Extraction with

Combined Expectation Maximization and Geodesic Active Contours," Signal Processing

and Information Technology, 2006 IEEE International Symposium on, pp. 107-111, 2006.

[34] P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion,"

IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 629-639, 1990.

42

[35] L. Ibanez, W. Schroeder, L. Ng and J. Cates, "The ITK Software Guide,"

[36] L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O.

Hall, R. W. Thatcher and M. L. Silbiger, "MRI segmentation: methods and applications,"

Magnetic Resonance Imaging, vol. 13, pp. 343-368, 1995.

[37] D. L. Pham, C. Xu and J. L. Prince, "Current methods in medical image

segmentation,” Annual Review of Biomedical Engineering, vol. 2, pp. 315-337, 2000.

[38] J. M. Henderson, K. Carpenter, H. Cartwright and G. M. Halliday, "Loss of thalamic

intralaminar nuclei in progressive supranuclear palsy and Parkinson's disease: clinical and

therapeutic implications,” Brain, vol. 123 ( Pt 7), pp. 1410-1421, 2000.

[39] J. Ashburner and K. J. Friston, "Voxel-based morphometry-the methods,”

Neuroimage, vol. 11, pp. 805-821, 2000.

[40] J. Ashburner and K. J. Friston, "Comments and controversies. Why voxel-based

morphometry should be used,” Neuroimage, vol. 14, pp. 1238-1243, 2001.

[41] K. J. Anstey and J. J. Maller, "The role of volumetric MRI in understanding mild

cognitive impairment and similar classifications,” Aging and Mental. Health, vol. 7, pp.

238-250, 2003.

[42] Y. S. K. Vetsa, M. Styner, S. M. Pizer, J. A. Lieberman and G. E. -. Gerig, “Caudate

Shape Discrimination in Schizophrenia using Template-Free Non-Parametric Tests,”

MICCAI, vol. 2879, pp. 661-669, 2003

43

[43] D. Goldberg-Zimring, A. Achiron, S. K. Warfield, C. R. G. Guttmann and H.

Azhari, "Application of spherical harmonics derived space rotation invariant indices to

the analysis of multiple sclerosis lesions' geometry by MRI," Magnetic Resonance

Imaging, vol. 22, pp. 815-825, 2004.

[44] G. Gerig, M. Styner, D. Jones, D. Weinberger and J. Lieberman, "Shape analysis of

brain ventricles using SPHARM," pp. 171-178, 2001

[45] R. Cabeza, N. D. Anderson, J. K. Locantore and A. R. McIntosh, "Aging gracefully:

compensatory brain activity in high-performing older adults,” Neuroimage, vol. 17, pp.

1394-1402, 2002.

[46] S. Ogawa, T. M. Lee, A. R. Kay and D. W. Tank, "Brain Magnetic Resonance

Imaging with Contrast Dependent on Blood Oxygenation," Proceedings of the National

Academy of Sciences, vol. 87, pp. 9868-9872, 1990.

[47] D. G. Norris, "Principles of magnetic resonance assessment of brain function,"

Journal Magnetic Resonance Imaging, vol. 23, pp. 794-807, 2006.

[48] D. J. Heeger and D. Ress, "What does fMRI tell us about neuronal activity?" Nature

Reviews Neuroscience, vol. 3, pp. 142-151, 2002.

[49] E. Amaro Jr and G. J. Barker, "Study design in fMRI: basic principles,” Brain Cogn.,

vol. 60, pp. 220-232, 2006.

[50] D. H. Brainard, "The Psychophysics Toolbox,” Spatial Visualization, vol. 10, pp.

433-436, 1997.

44

[51] S. C. Strother, "Evaluating fMRI preprocessing pipelines,” IEEE Engineering in

Medicine Biology and. Magnetic, vol. 25, pp. 27-41, 2006.

[52] J. V. Hajnal, R. Myers, A. Oatridge, J. E. Schwieso, I. R. Young and G. M. Bydder,

"Artifacts due to stimulus correlated motion in functional imaging of the brain,"

Magnetic Resonance Medicine, vol. 31, pp. 283-291, 1994.

[53] S. C. Strother, J. R. Anderson, X. L. Xu, J. S. Liow, D. C. Bonar and D. A.

Rottenberg, "Quantitative comparisons of image registration techniques based on high-

resolution MRI of the brain," Journal of Computer Assisted Tomography, vol. 18, pp.

954-962, 1994.

[54] T. R. Oakes, T. Johnstone, K. S. Ores Walsh, L. L. Greischar, A. L. Alexander, A. S.

Fox and R. J. Davidson, "Comparison of fMRI motion correction software tools,"

Neuroimage, vol. 28, pp. 529-543, 2005.

[55] R. Liao, J. L. Krolik and M. J. McKeown, "An information-theoretic criterion for

intrasubject alignment of FMRI time series: motion corrected independent component

analysis,” IEEE Transaction on Medical Imaging, vol. 24, pp. 29-44, 2005.

[56] H. J. Jo, J. Lee, J. Kim, Y. Shin, I. Kim, J. S. Kwon and S. I. Kim, "Spatial accuracy

of fMRI activation influenced by volume- and surface-based spatial smoothing

techniques," Neuroimage, vol. 34, pp 540-564, 2007.

[57] K. J. Worsley, "An overview and some new developments in the statistical analysis

of PET and fMRI data,” Human Brain Mapping, vol. 5, pp. 254-258, 1997.

45

[58] M. Reimold, M. Slifstein, A. Heinz, W. Mueller-Schauenburg and R. Bares, "Effect

of spatial smoothing on t-maps: arguments for going back from t-maps to masked

contrast images,” Journal of Cerebral Blood Flow Metabolism, vol. 26, pp. 751-759,

2006.

[59] A. Geissler, R. Lanzenberger, M. Barth, A. R. Tahamtan, D. Milakara, A. Gartus and

R. Beisteiner, "Influence of fMRI smoothing procedures on replicability of fine scale

motor localization," Neuroimage, vol. 24, pp. 323-331, 2005.

[60] K. J. Friston, A. Mechelli, R. Turner and C. J. Price, "Nonlinear responses in fMRI:

the Balloon model, Volterra kernels, and other hemodynamics,” Neuroimage, vol. 12, pp.

466-477, 2000.

[61] O. Friman, J. Cedefamn, P. Lundberg, M. Borga and H. Knutsson, "Detection of

neural activity in functional MRI using canonical correlation analysis,” Magnetic

Resonance in Medicine, vol. 45, pp. 323-330, 2001.

[62] M. J. Mckeown, S. Makeig, G. G. Brown, T. P. Jung, S. S. Kindermann, A. J. Bell

and T. J. Sejnowski, "Analysis of fMRI data by blind separation into independent spatial

components," Human Brain Mapping, vol. 6, pp. 160-188, 1998.

[63] J. Talairach and P. Tournoux, Co-Planar Stereotaxic Atlas of the Human Brain: 3-

Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme, 1988,

[64] F. Crivello, T. Schormann, N. Tzourio-Mazoyer, P. E. Roland, K. Zilles and B. M.

Mazoyer, "Comparison of spatial normalization procedures and their impact on

functional maps," Human Brain Mapping, vol. 16, pp. 228, 2002.

46

[65] C. E. Stark and Y. Okado, "Making memories without trying: medial temporal lobe

activity associated with incidental memory formation during recognition,” Journal of

Neuroscience, vol. 23, pp. 6748-6753, 2003.

[66] M. I. Miller, M. F. Beg, C. Ceritoglu and C. Stark, "Increasing the power of

functional maps of the medial temporal lobe by using large deformation diffeomorphic

metric mapping," Proceedings of the National Academy of Science U. S. A., vol. 102,

pp. 9685-9690, 2005.

[67] P. A. Yushkevich, J. A. Detre, D. Mechanic-Hamilton, M. A. Fernandez-Seara, K. Z.

Tang, A. Hoang, M. Korczykowski, H. Zhang and J. C. Gee, "Hippocampus-specific

fMRI group activation analysis using the continuous medial representation,"

Neuroimage, vol. 35, pp. 1516-1530, 2007.

[68] D. V. Vranic, "An improvement of rotation invariant 3D-shape based on functions

on concentric spheres," in 2003, pp. III-757-60 vol.2, 2003

[69] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, pp. 156-65, 2003.

[70] V. Caselles, “Geodesic active contours,” International Journal of Computer Vision

(IJCV), vol. 22, no. 1, pp. 61–79, 1997.

47

2 Unique Invariant SPHARM Features for ROI Based

Analysis 1

2.1 Introduction

Magnetic resonance imaging (MRI) is increasingly recognized as a suitable modality for

studying the human brain anatomy in vivo. Improvements in both MRI scanner hardware

and acquisition sequences are yielding progressively higher resolution 3D images of

internal brain structures. One of the main benefits of this increased resolution is in the

study of structure of brain anatomy. Researchers use MR images to delineate specific

brain areas, like the thalamus, to observe structural changes either over time or across two

or more subject groups, e.g. patients with Parkinson’s disease (PD) and normal

volunteers. This process of delineating specific structures to perform targeted analysis is

termed region of interest (ROI) analysis.

Numerous methods have been proposed to quantify and analyze the shape of ROIs. The

simplest and most common approach uses the overall volume within an ROI, e.g. Anstey

et al used the hippocampal volume to investigate changes observed in mild cognitive

impairment (MCI) [1]. However, studies using volumetric measures do not reflect actual

shape changes that might occur which might be indicative of neurological change. Vetsa

et al. used medial representations to characterize the surface of the caudate and identify

1A version of this chapter has been published. Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ, “Invariant SPHARM Shape Descriptors for Complex Geometry in MR Region of Interest Analysis” 29th Annual International Conference IEEE Engineering in Medicine and Biology Society 2007, pp. 1322-1325, France 2007

48

shape changes in schizophrenia [2]. However, this approach requires accurate alignment

of the ROIs across different subjects for valid analysis and hence residual errors in

mutual alignment could adversely affect the final results. Alternate methods rely on

obtaining descriptive feature vectors which may reflect the structural information in an

ROI. These features may be invariant to rotations, translations and scale, thus enabling

easy comparison across different subjects. This eliminates the need for mutual alignment,

saving time and potential inconsistencies arising from registration errors. In an earlier

work, we used scale, rotation and translation invariant features derived using a spherical

harmonic (SPHARM) representation of 3D ROIs to analyze shape changes in brain MRI

data [3] and demonstrated the advantages of using such an approach along with

traditional volumetric analysis. However, the parameterization technique used in our

previous work did not allow for shapes with non-convex topology. In this paper, we

extend our method and propose new enhanced SPHARM shape descriptors that are

unique to any ROI. These features also enable the characterization of complex shapes

with complex topology, including those with multiple disjoint parts. We validate our

method on synthetic data and demonstrate the effectiveness of the proposed technique

even in the presence of inter-subject variability and misalignment between subjects. We

also use the proposed technique to investigate shape changes in the thalamus in patients

with Parkinson’s disease.

2.2 Methods

In this section, we briefly summarize our earlier work on SPHARM-based ROI

descriptors in MRI. We then proceed to present the proposed enhancements used to

49

enable the study of complex ROI topologies including a novel radial transform used to

obtain unique features for any ROI.

2.2.1 Proposed Invariant SPHARM features

A 3D ROI with spherical topology can be expressed as ),( , a function defined on the

unit sphere with and as the zenithal and azimuthal angles respectively. The value of

the function at a given ( , ) is equal to the distance to the surface point from the

centroid at those angles [3]. The SPHARM representation of this function is given by 2.1.

(2.5)

),(* lmY is the complex conjugate of the mth order spherical harmonic of degree l, where

l ranges from 0 to L [4]. The accuracy of this representation depends on the value of L,

also called the bandwidth.

Invariance of the representation to translation is obtained by shifting the origin of the

3D ROI to its centroid before computing the SPHARM coefficients. In our previous work

[3], we employed rotationally invariant features from this representation using (2.2).

Scale normalization was achieved by scaling the vector obtained in (2.2) with its first

element, which gives a rough measure of total volume [3].

(2.6)

Non convex topologies, i.e. surfaces with self occlusions, or topologies with disconnected

components (e.g. ventricles) cannot be represented as a function of two variables, ),( 50

, since these topologies do not always have a single distance value for all ( , ). A third

variable r, the distance from the origin can be introduced to extend the definition to

include such shapes. The augmented function ),,( r is then binary valued, taking a

non-zero value only in points inside the 3D ROI. The SPHARM representation of such a

function is given by:

(2.7)

k is an index introduced to account for possible degeneracy [4]. Since direct computation

of (2.3) is highly inefficient, we use an alternate approach by representing the data as a

set of spherical functions. These functions are obtained by intersecting the 3D binary ROI

with R spherical shells of increasing radii r. This intersection is simulated by sampling

the 3D ROI on a spherical grid of constant dimensions 2L2L at each value of r [5]. The

SPHARM coefficients are then obtained at each value of r as:

(2.8)

This results in a SPHARM representation for each shell. Invariant features for these

shells can then be derived using (2.2), as used by Kazhdan et al [6]. However, as noted in

[6], this representation is not unique, since independent rotations of the shape along any

of the constituting shells will result in the same feature vector representation even though

the topologies of the shapes are drastically different. To overcome this limitation, we

propose adapting the radial transform in (2.3) across these features as in (2.5). This yields

unique features even under independent rotations along the shells. To achieve scale

51

invariance across different ROIs, we propose to keep the number of shells, R, constant at

2Rmax for all ROIs being analyzed. Rmax is the radius measure in voxels of the smallest

common sphere encompassing each of the ROI in the entire set being analyzed.

(2.9)

Since this radial transform is applied across each value of r, as shown in (2.5), the vector

must be of the same length for each shell. Hence, we use a common value of L for all

shells, whose minimum value is obtained by equating the surface area of the

encompassing sphere to the equiangular sampling grid (2.6).

max2max ,224 RLLLR (2.10)

The final unique, scale, translation and rotation invariant features are defined as in (2.7).

These values are then reshaped into a single row to provide the final feature vector.

(2.11)

Figure 2.1 shows how this method could be used to analyze complex disconnected 3D

ROIs like the human brain ventricles.

52

Figure 2.14 (a) The human brain ventricles. The two ventricles would have to be analyzed jointly since the relative orientations might be of importance. One of the

spherical shells at r =35 is also shown. (b) The parameterization of the surface at r = 16 (top) and 35 (bottom)

2.2.2 Statistical Analysis of Features

The feature vectors thus obtained are of a high dimension, dependent on the value of L

chosen. Moreover, the generating probabilities of these features are unknown. We thus

employ a non-parametric permutation test for the statistical analysis of these features,

since no assumptions of the feature parameters are required.

In permutation tests, a distance measure between two groups of shapes (represented by

their feature vectors) is tested against the distance obtained by all possible permutations

of the vectors across the two groups. We use the Euclidian distance between the feature

vectors as the distance measure. Also, as reported by Vetsa et al [2] we use a Monte Carlo

approach to obtain a sufficiently high number of permutations, since testing against all

53

possible permutations is not feasible. A final p value is obtained as the ratio of the

number of permutations which yielded a Euclidian distance greater than the original

ordering of the samples and the total number of permutations performed. If the obtained p

value is less than a statistical standard threshold of 0.05, the two groups are declared to

have significant differences between them. In our study, this is a strong indication that the

shapes in the two groups have a systematic difference in structure.

2.3 Data and Imaging

This section describes the generation and acquisition of data used to test our proposed

approach, which include synthetic validation data as well as real structural MRI data of

patients and controls.

2.3.1 Synthetic Structural Data Generation

To verify the performance of the proposed shape description technique, we test on

synthetic data with simulated, but nevertheless realistic inter-subject variability. Similar

to [7], the basic shape used to generate these data is an ellipsoid as defined in (2.8) where

(xc, yc, zc) is the centroid with (a, b, cX) as parameters defining the 3D boundary of the

ellipsoid.

(2.12)

Keeping a and b constant, two values of cX, ca and cb, were used to generate two groups

of shapes, A and B. Twenty samples of these shapes were created in each group. A

common centroid of (64, 64, 64) was chosen in a grid of (128, 128, 128) for both groups,

54

keeping with the resolution of real data. Each sample was independently created by

perturbing the centroid using (nxi, nyi, nzi), generated from a Gaussian noise source with

zero mean and a standard deviation of 5, N(0,5). The parameters (a, b, cX) were perturbed

by (nai, nbi, nci) generated from N (0, 0.2). The ellipsoid was then rotated about a random

combination of x, y, and/or z axis by an angle generated by a uniform distribution from

045˚. To create a realistic surface, comparable to the irregular edges obtained from

manual ROI segmentation, we add Gaussian noise of N (0, 05) and use a set of

morphological operations to obtain the final shape shown in Figure 2.2.

Figure 2.15 (a) Surface rendering of a real left thalamus (top) and right thalamus (bottom) from a PD patient, note the rough edges. (b) Group A synthetic samples (see text)

generated with parameter set (2, 5, 10). (c) Group B synthetic sample generated with parameter set (2, 5, 8). Note the realistic looking edges in the synthetic data.

2.3.2 Real Structural MR Data Acquisition

The data used in this study consisted of MRI scans of 21 control subjects and 19 PD

patients. Two scans were performed with a gap of two hours, one before and one after the

administration of the drug L-dopa. The MR data were acquired on a 3.0 Tesla Siemens

55

scanner (Siemens, Erlangen, Germany) with a birdcage type standard quadrature head

coil and an advanced nuclear magnetic resonance echoplanar system. The participant’s

head was positioned along the canthomeatal line. Foam padding was used to limit head

motion within the coil. High-resolution T1 weighted anatomical images (3D SPGR,

TR=14ms, TE=7.7 ms, flip angle=25°, voxel dimensions 1.0×1.0×1.0mm, 176×256

voxels, 160 slices) were acquired.

ROIs for the left and the right thalamus were manually drawn on both the scan data sets

using the IRIS 2000 software (NeuroLib, University of North Carolina) by a trained

research assistant using a computer mouse. The research assistant was blinded to the

disease category.

2.4 Results and Discussion

This section presents quantitative results of employing the proposed SPHARM shape

features on the synthetic and real MR data outlined in Section 2.3.

2.4.1 Validation on Synthetic Data

Synthetic data generated as described earlier consisted of forty one data sets each set

having two groups, A and B, each group with twenty sample shapes. For the entire set,

group A was re-generated independently each time with a baseline parameter set (2, 5,

10). Group B was generated using a different baseline parameter set each time, starting

with (2, 5, 8) and ending with (2, 5, 12), with the value of cb being incremented by 0.1 for

each set. The proposed SPHARM invariants were then derived for all samples in each set.

Rmax was found to be22; hence 44 shells were used to parameterize the ROIs. A value of

40 was chosen for L as per (2.6), resulting in a feature vector length of 1760 elements. 56

The Euclidian distance between the SPHARM features of the two groups, A and B, in

each set, was recorded. Permutation tests were then performed for each set to determine

the level of significance in the difference between the features of the two groups. Figure

2.3 summarizes the results of this analysis.

Figure 2.16 Plot of the Euclidian distance between the two groups A and B for different values of cb. Distances resulting in a significant difference (alpha = 0.05) between the groups as obtained by the permutation test are indicated with a star. Non-Significant

distances are indicated with a dot.

The graph in Figure 2.3 shows the expected trend in the Euclidian distance measure

between the two groups. For values of cb smaller than 9.5 and larger than 10.6, the

features are able to detect a systematic difference in shape between the two groups.

However, as the value of cb approaches 10 (the value of ca), there is less difference in the

sample shapes between the two groups. For values of cb in the range (9.5, 10.6), the

combined effect of the various perturbations in the parameters involved, coupled with the

57

inter-subject variability introduced, leaves almost no difference in constituting shapes of

the two groups. This is shown in Figure 2.3 with dots, indicating that the permutation test

was unable to find any systematic difference in the features vectors. This experiment

demonstrates the sensitivity of the proposed technique in discriminating subtle shape

changes between two groups.

2.4.2 Analysis of Real MR Structural Data

The proposed technique was next used to analyze the structure of the left and the right

thalamus in patients with Parkinson’s disease. SPHARM features were computed for the

data of 21 control subjects and 19 PD patients. Rmax was found to be 20 voxels; hence 40

shells were used to parameterize the ROIs. The bandwidth L was chosen to be 36 as per

(2.6), resulting in a feature vector length of 1440. Since two scans were performed for

each subject, two feature vectors were obtained for each ROI, for each subject. Also,

since the duration between the scans was less than two hours, no systematic structural

changes were expected between these two observations. The only changes expected were

due to repositioning, manual tracing inconsistencies and other imaging artifacts. To

confirm this assumption, each subject group (Patients and Controls) was further sub-

divided into two categories: pre-drug and post-drug. Permutation test results of the

SPHARM feature vectors between these two sub-groups are shown in Table 2.1. Results

from the volumetric analysis are also shown.

58

Table 2.3 Results of pre-drug vs. post-drug analysis

Subject group ROISPHARM

(p Value)

Volumetric

(p Value)

Controls Left Thalamus 0.3863 0.3270

Controls Right Thalamus 0.2828 0.2720

PD Left Thalamus 0.4738 0.2430

PD Right Thalamus 0.2341 0.3208

The results in Table 2.1 indicate that, as expected, there are no statistically significant

changes in the shape of the thalamus between the two scans. Having established this, the

two feature vectors from the two sessions were then averaged to generate a single feature

vector for each ROI for each subject. Direct averaging is valid since these features

represent the same shape. Changes due to rotation and translations are annulled by the

invariance property of the features. This averaging reduces the variability caused by

manual tracing errors and other noise sources, thereby increasing the sensitivity of the

features to actual shape changes. A permutation test on the averaged features was then

performed between the two subject groups. Results are indicated in Table 2.2; results

from the volumetric analysis are also shown.

59

Table 2.4 Results of PD patients vs. controls analysis

ROI SPHARM (p value) Volumetric (p value)

Left Thalamus 0.0012* 0.0102*

Our earlier work [3] on a smaller number of subjects observed differences in the volume

of both the thalamus in patients with PD, when compared against healthy volunteers.

However, the previous technique was unable to detect significant shape changes between

the groups. In this present study, in addition to the changes observed with volumetric

measures, we detect a significant difference in the shape of both thalami. The shape

analysis is independent of the volume changes observed since the features derived are

scale invariant. The new parameterization approach coupled with the increased number of

subjects probably contributed to this increased sensitivity. The results indicate that PD

patients studied have a marked difference in the volume of their thalamus when compared

to control subjects, indicating possible atrophy of this structure. Further work is required

to determine if the consistent atrophy in PD subjects corresponds to specific thalamic

nuclei (substructures within the thalamus).

2.5 Conclusions

We enhanced our earlier work generating invariant SPHARM features for 3D ROI

analysis in MR data by extending our characterization capability to ROIs with complex

topologies, including those with possible disconnections. We also proposed the use of a

novel radial transform to obtain unique feature. The proposed features were able to detect

subtle shape changes in synthetically created data with realistic inter-subject variations 60

and detect shape changes in the thalami of PD patients in addition to the volumetric

changes observed. The use of the proposed method to explore shape changes of different

brain structures as a biomarker of disease progression warrants further study.

61

2.6 References

[1] K. J. Anstey and J. J. Maller, "The role of volumetric MRI in understanding mild

cognitive impairment and similar classifications,” Aging Mental Health, vol. 7, pp.

238-250, 2003.

[2] Y. S. K. Vetsa, M. Styner, S. M. Pizer, J. A. Lieberman and G. E. -. Gerig, “Caudate

Shape Discrimination in Schizophrenia using Template-Free Non-Parametric Tests”

in MICCAI 2003, vol. 2879, pp. 661-669, 2003.

[3] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs. volume:

Invariant shape descriptors for 3D region of interest characterization in MRI," in

ISBI, pp. 754-757, 2006.

[4] G. Burel and H. Henocq, "Three-dimensional invariants and their application to

object recognition,” Signal Process, vol. 45, pp. 1-22, 1995.

[5] D. M. Healey Jr, D. N. Rockmore and S. B. Moore, "An FFT for the 2-sphere and

applications," in ICASSP 1996, pp. 1323-1326 vol. 3, 1996.

[6] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, 23-25 June 2003, pp. 156-65, 2003

62

[7] D. Goldberg-Zimring, A. Achiron, S. K. Warfield, C. R. G. Guttmann and H. Azhari,

"Application of spherical harmonics derived space rotation invariant indices to the

analysis of multiple sclerosis lesions' geometry by MRI," Magnetic Resonance

Imaging, vol. 22, pp. 815-825, 2004.

63

3 Detection and Analysis of Anatomical Shape Changes

in MRI (PD thalamus)2

3.1 Background

The thalamic changes seen in Parkinson Disease (PD) may represent selective non-

opaminergic degeneration [1], as there is selective neuronal loss in the centre median-

parafascicular (CM-Pf) complex in Parkinson's disease [2], yet relative preservation of

neurons in the limbic (mediodorsal and anterior principal) thalamic nuclei. Henderson et

al. examined the thalamic intranuclear nuclei in 10 normal controls and 9 patients with

PD [3]. As expected, they found α-synuclein-positive Lewy bodies in these nuclei in the

thalamus, but they also found a significant reduction (40-55%) in the total neuronal

number in the caudal intralaminar (CM-Pf) nuclei, regions that receive glutaminergic

innervation [3]. This contrasted with the 70% loss of pigmented nigral neurons. A factor

analysis has demonstrated that the size of neurons in the motor cortex is negatively

correlated with the size and number of neurons in its thalamic relay, the VLp. There is

also a positive correlation between the number of ventral anterior (VA) neurons and the

pre- supplementary motor area (SMA) [4].

2A version of this chapter has been submitted for publication. Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer, Mechelle Lewis and Xuemei Huang, “Shape (But Not Volume) Changes in the Thalami in Parkinson Disease”, Submitted to BioMed Central Neuroscience, 2007A version of this chapter has been accepted for a poster presentation. Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer, Mechelle Lewis and Xuemei Huang, "MRI in Parkinson's Disease identifies shape, but not volume changes in the thalamus", Abstract, Selected for poster presentation at XVII WFN World Congress on Parkinson's Disease and Related Disorders, Amsterdam, The Netherlands, 2007

64

Bacci et al. suggested that CM-Pf degeneration may partially counteract the

consequences of dopamine neuronal loss, as thalamic and dopamine inputs have

antagonistic influence on neurotransmitter-related gene expression [1]. Moreover, the

CM-Pf degeneration may be a direct consequence of nigrostriatal denervation, as

depleting the striatum of dopamine results in the remaining Pf neurons being particularly

hyperactive [5].

The normal role of the CM-Pf complex is incompletely understood, although it is clearly

related to basal ganglia function [6]. The Pf nuclei receive input from the spinal cord and

project to the striatum [7]. These projections may carry specific temporally-patterned

inputs to striatal targets [8]. While the CM-Pf complex has traditionally been considered

part of the reticulo-thalamo-cortical activating system, a recent proposal suggests that the

CM-Pf complex participates in sensory driven attention processes, particularly

unexpected events [9].

The advent of modern imaging techniques has allowed the non-invasive in vivo

assessment of brain structures, such as the thalamus, in disease states. Thalamic

morphological changes have been detected chronically after cortical injury, such as

middle cerebral artery (MCA) infarction after 1 yr [10, 11] and tumor resection after

~2yrs [12]. The study by Hulshoff Pol [12] detected a 5% decrease in ipsilateral

thalamus and, interestingly, a 4.5% increase in contralateral thalamic volume after

unilateral tumor resection, presumably on the basis of a compensatory mechanism.

In PD and related disorders, some studies of structural and functional imaging have

detected thalamic changes. Thalamic grey matter changes have been detected

65

contralateral to unilateral Parkinsonian resting tremor [13]. In PD with dementia, the

thalamus, in addition to the hippocampus and anterior cingulate, represent the regions

most affected [14]. Functionally, there is a connection between a major component in F-

DOPA uptake in the striatum and a component from fluoro-deoxy--glucose (FDG), which

had positive loadings in the thalamus and the cerebellum [15].

Most morphological studies based on imaging involve a number of steps manipulating

the brain images. A typical approach would be to warp ("spatially normalize") the brain

images to a common space [13]. Further smoothing of the data (e.g. using an isotropic

12mm Gaussian kernel) to minimize the effects of misregistration between different

normalized brains may affect the ability to make inferences about small, subcortical

structures like the thalamus. In fact this "Voxel Based Morphometry" approach has thus

been a controversial approach (e.g., see discussions in [16] and [17]).

Recent approaches try to reduce errors due to misregistration by aligning the subjects at

the region of interest (ROI) level, as opposed to the whole brain level [18] [19] [20].

However, these approaches are designed to deal with a different problem, namely that of

summarizing fMRI activation from several subjects. To quantify differences in

morphology, it would be necessary to examine the different transformations required to

warp each subject's ROIs to the exemplar ROI shape -- a non-trivial task.

An alternative approach to warping brains to the same space is to segment brain

structures individually on unmanipulated (i.e. unregistered and unwarped) brains [21].

Because no registration of the brain images is done, this requires summarizing the

individual brain structures in a way that they are invariant to positioning of the head in

66

the scanner. For example, simply estimating the volume of an ROI such as the thalamus

has this property, as it is invariant to the individual coordinate frame used. A number of

such invariants (e.g. spatial variance) have been proposed to summarize the shape of

brain structures [22], or even characterize the distribution (texture) of activation maps in

fMRI [23].

We have recently proposed a method based on spherical harmonics (SPHARM) which

provided a unique representation of brain structures, including regions with possible

topological disconnections, such as the lateral ventricles [24]. In brief, the method

involves first finding a spherical shell which encompasses the entire ROI. Subsequent

smaller concentric shells are then derived and the intersection between the progressively

smaller spherical shells and the brain structure is computed (Figure 3.1). The results from

the intersections are then combined into a unique feature vector containing approximately

100's or 1000's of elements. This feature vector provides a unique representation of the

shape which is independent of the spatial orientation of the structure (see section 3.5).

We examined the thalami from 18 PD subjects and 18 age-matched controls. Using the

above technique, we found significant differences between the two groups in the shape of

the thalami, but not in the volume. This suggests that significant thalamic changes can be

assessed noninvasively in PD, suitable for longitudinal studies.

67

Figure 3.17 The SPHARM-based method for shape determination. The shape to be specified (the thalamus) and two concentric spherical shells are shown. On the right is the intersection between the thalamus and shells as a function of rotation (θ) and azimuth (φ).

The rotation angle spans from 0 to 2π radians, and the azimuth angle is from 0 to π radians.

3.2 Results

There were no significant differences in volume between sides in either controls or PD

subjects, nor between controls and PD subjects in either the left or right thalamus (Table

3.1). In contrast, the SPHARM-based method found significant shape differences

between the left and right thalamus in PD but not in controls. Significant shape

differences between PD and controls were detected in both the left and right thalami.

68

Table 3.5 Results of volumetric and shape analysis. Numbers indicate the p-values obtained from the permutation test

Group Volume SPHARM

Control, Left vs. Right 0.5630 0.1470

PD, Left vs. Right 0.5780 0.0060

Left thalamus, PD vs. Control 0.4150 0.0270

Right thalamus, PD vs. Control 0.1730 0.0290

Multivariate regression did not find any statistically significant (p < 0.05) effects of

handedness, side of symptoms, or dominant side of tremor on the distance measure.

In order to better visualize and intuitively assess the shape differences in thalami between

PD subjects and controls, we took thalami that had "typical" feature vectors (i.e. feature

vectors closest to the mean of each group) and assumed that they represented exemplar

shapes. We then spatially aligned these exemplar shapes (Figure 3.2). There appeared to

be greater differences in the left thalami between controls and PD subjects. The largest

differences appeared to be along the dorsal surface. Note that the registration of the

thalami in this instance was solely for visualization purposes and was not incorporated

into the analysis.

69

Figure 3.18 Two sets typical thalami registered and shown on brain from a PD subject. Note that the registration here is solely for visualization purposes, and is not required for the calculation of shape differences. Also, although the thalami here were first smoothed

with a 12mm FWHM Gaussian kernel for visualization purposes, no smoothing was performed for the shape analysis and group comparison.

70

3.3 Discussion

It is well known that changes in the thalamus can be seen chronically after cortical injury

[25, 26]. This is not only due to direct effects of axonal damage, as axonal-sparing

cortical lesions also result in thalamic degeneration [27]. Such thalamic degeneration

probably involves both anterograde and retrograde processes [28] and may be mitigated

by growth factors [29] [30]. Brain development has a critical role on the extent of

thalamic changes after a cortical lesion. Animal models have determined that perinatal

lesions are far less likely to induce thalamic changes, compared to when the cortical

lesions are made prenatally [31] or in adulthood [32]. . In contrast to the secondary

effects of thalamic changes from cortical lesions, the thalamic changes in PD are related

to selective non-dopaminergic neurodegeneration [1].

Consistent with prior results, we found no significant differences in the volume of the

thalami between PD subjects and controls [3]. However, for the first time, we have

demonstrated that the shape of the thalami undergoes systematic changes in PD. The

reason that shape may change but not the volume may be due to the fact that particular

nuclei (e.g. CM-Pf) are involved, and thus, at the typical resolution of MRI, this does not

result in significant changes in the overall volume. Alternately, since thalamic volume

may actually increase as a compensatory mechanism [12], other regions of the thalamus

may hypertrophy.

The ability to non-invasively quantify subtle morphological shape changes appears to be

a powerful technique. We utilized standard structural MR imaging techniques without

71

any special sequences or any special scanner resolution requirements. We obtained robust

results from pooling data from two different centers using two different types of scanners.

We used manual segmentation of the thalami in this paper. Automatic segmentation of

subcortical structures is an area of ongoing research [33], and often requires the tuning of

many parameters, especially when the images may be pooled from scanners from

different centers. Since the person at each centre doing the segmentation was blinded to

disease status, it would be unexpected that a systematic bias was introduced into our

results. Even then, any misspecification of the same ROI across subjects would tend to

increase inter-subject variability and presumably reduce discriminability across groups

making the task harder for the shape analysis approach.

We used SPHARM-based invariant descriptors to quantify the shape of the thalami. The

main advantages of such a method is that it does not require that all brain images be

warped to a common space, nor does it require that the brain images be aligned in any

way. A drawback of these invariant features approach is that it is difficult to invert the

feature vectors, i.e. once given all the values of the different invariants, it is impossible to

reconstruct the original image which gave that feature vector -- analogous to the fact that

given the volume of an object, it is impossible to uniquely reconstruct the original shape.

We therefore cannot create a "typical" brain structure by averaging the feature vectors

and create the image that would give this feature vector (e.g. to create an "average left

thalamus"). However, it is possible to cluster structures in the feature space and find the

brain structure whose feature vector is in the middle of the cluster so as to use it as an

exemplar shape, which we have done (Figure 3.2).

72

It is difficult to determine if the shape differences we detected are attributable to any

specific nuclei. However, based on prior pathological studies, it would be likely that the

differences we detected were related to degeneration in the CM-Pf complex. Given that

progressive supranuclear palsy (PSP) has even greater involvement of VLp than PD [4],

it remains to be seen if thalamic shape is a discriminable feature between these two

conditions.

We did not detect any association between overall shape change and handedness, and

dominant side presentations or presence/absence of tremor. This may be due to the

relatively small sample size employed in this study. However, because the feature vectors

consist of many different components, we don't discount that there may be a subset of

components that are sensitive to these disease parameters.

3.4 Conclusions

Our results suggest that systematic changes in thalamic shape can be non-invasively

assessed in PD in vivo and that shape changes, in addition to volume changes, may

represent a new avenue to assess the progress of neurodegenerative processes. Although

we cannot state which parts of the thalamus are directly affected, previous pathological

studies would suggest that the shape changes detected in this study represent

degeneration in the centre median-parafascicular (CM-Pf) complex, an area known to

represent selective non-dopaminergic degeneration in PD.

73

3.5 Methods

The study was approved by the appropriate Institutional Review Boards and Ethics

Boards of the University of British Columbia (UBC) and the University of North

Carolina (UNC). All structural data were obtained as part of fMRI studies whose results

are reported elsewhere (e.g., [34]).

3.5.1 MR Imaging at the University of British Columbia

All subjects gave written informed consent prior to participating. Nine volunteers with

clinically diagnosed PD participated in the study (5 men, 4 women, mean age 68.1 6.8

years, 7 right-handed, 2 left-handed). All subjects had mild to moderate PD (Hoehn and

Yahr stage 2-3) [35] with mean symptom duration of 3.6 2.6 years. We recruited ten

healthy, age-matched control subjects without active neurological disorders (3 men, 7

women, mean age 55 ± 12.4 years, 9 right-handed, 1 left-handed). Exclusion criteria

included atypical Parkinsonism, presence of other neurological or psychiatric conditions

and use of antidepressants, sleeping tablets, or dopamine blocking agents.

MRI was conducted on a Philips Achieva 3.0 T scanner (Philips, Best, The Netherlands)

equipped with a head-coil. A high resolution, three dimensional (3D) T1-weighted image

consisting of 170 axial slices was acquired of the whole brain to facilitate anatomical

localization of activation for each subject.

The thalami were one of eighteen specific regions of interest (ROIs) that were manually

drawn on each unwarped, aligned structural scan using the Amira software (Mercury

Computer Systems, San Diego, USA). Although the thalami were manually segmented

on the axial slices, they were carefully examined in the coronal and saggital planes to 74

ensure accuracy. The trained technician performing the segmentation was blinded to the

disease state.

3.5.2 MR Imaging at the University of North Carolina

All subjects gave written informed consent prior to participating. Nine volunteers with

clinically diagnosed mild to moderate PD (Hoehn and Yahr stage 2-3 -- mean symptom

duration of 2.1 2.0 years) participated in the study (5 men, 4 women, mean age 58

12yrs, all right-handed). We also recruited eight healthy, age-matched control subjects

without active neurological disorders (5 men, 3 women, mean age 49 14yrs, 8 right-

handed). Images were acquired on a 3.0 Tesla Siemens scanner (Siemens, Erlangen,

Germany) with a birdcage-type standard quadrature head coil and an advanced nuclear

magnetic resonance echoplanar system. The head was positioned along the canthomeatal

line. Foam padding was used to limit head motion. High-resolution T1 weighted

anatomical images were acquired (3D SPGR, TR=14 ms, TE=7700 ms, flip angle=25˚,

voxel dimensions 1.0 x 1.0 x 1.0 mm, 176x256 voxels, 160 slices).

ROIs (including thalami) were drawn manually by the same trained research associate

with assistance from multiple on-line and published atlases (e.g. [36]).

3.5.3 Thalami Shape Analysis

As described in the technical appendix, the analysis of each shape results in a unique

feature vector, of length n = 1440. The left and right thalami were analyzed separately.

75

For comparison, we examined for any differences in volume. The volume of each

thalamus was estimated as the number of voxels that each ROI contained multiplied by

the volume of a single voxel.

To assess the significance of group differences between feature vectors, we used a

permutation test to generate a null distribution of Euclidean distances between feature

vectors. The permutation test does not require a priori assumptions about the data

distribution, and is thus preferred over T-test and F-test [37]. We assessed the differences

in left vs. right thalami in controls, left vs. right in PD subjects, PD vs. controls for the

left thalamus, and PD vs. controls for the right thalamus.

3.5.4 Shape Analysis -- Technical Aspects

Let be a function defined on the unit sphere with and as the zenithal and

azimuthal angles, respectively. The SPHARM representation for this function is given by

(3.1) where is the complex conjugate of the mth order spherical harmonic of

degree l. l ranges from 0 to L [16]. Increasing the value of L, also called the bandwidth,

improves the representation accuracy at the cost of higher computation time. This

definition can also be extended to real valued 3D distributions (3.2), where r is

the distance from the origin to a given voxel. k is an index introduced to account for

possible degeneracy due to the additional dimension [38].

dYdc lmml sin,,

2

0 0

* (3.13)

76

0 0

*2

0

2 sin,,,sin2

drYr

krddrrc lmmkl

(3.14)

As explained later in this section, rotationally invariant features can be derived from this

spherical harmonic representation. In our application, we also need the features to be

invariant to any translation of the entire ROI in 3D space. To achieve this, we move the

origin of the function , to the centroid of , where is given

by (3.3).

(3.15)

Since direct computation of (3.2) is highly inefficient [39], we use an alternate approach

by representing the data as a set of spherical functions obtained by intersecting the 3D

data with spherical shells. Alternatively, for each value of r, can be visualized

as a spherical shell comprising the function values at a distance r from the origin. r can

then be incremented in steps of t to encompass the entire ROI. If the initial representation

of the function is in the form of a cubic grid (regular isotropic voxels in our case),

volumetric interpolation is required to resample the ROI in the spherical coordinate

space.

When analyzing multiple subjects’ ROIs simultaneously, we define the maximum radius,

Rmax, as the minimum radial distance in voxel count that encompasses all non-zero values

of all subjects’ ROIs being analyzed. To represent the values from the cubic grid of all

77

ROIs with sufficient accuracy, 2Rmax shells are used. To achieve scale invariance, the

shells must be distributed evenly throughout the spatial extent of each ROI. Since the

ROI size across subjects is not uniform, shell spacing t must be adjusted for each subject

separately. This procedure ensures that each shell captures similar features from the 3D

ROI irrespective of its scale.

Surface sampling along each of these shells is performed on an equiangular spherical grid

of dimensions 2L×2L [39]. The common bandwidth L for all shells of all functions is

chosen to satisfy the sampling criterion for the largest shell in this set of ROI, namely the

one with radius Rmax. The surface area for this shell represents the maximum surface shell

area that needs to be sampled by the equiangular grid; hence, any value of L satisfying the

required equiangular sampling (2L×2L) at this shell will be sufficient to represent data

from smaller radii shells. The minimum value for L is obtained by equating the surface

area of this largest shell to the equiangular sampling grid (3.4). Higher values of L are not

used, since it increase computation time with no added benefit. Also, this will result in

longer feature vectors, complicating the analysis. Furthermore, when the represented

object is a discrete array, higher values of l, resulting from a larger L, may correspond to

sampling noise [38]. Recognizing that in applications pertaining to discrimination, high

accuracy in the SPHARM representation is not a necessity, we chose to use the minimum

value for L as that obtained by (3.4).

max2max ,224 RLLLR (3.16)

To obtain the SPHARM representation for all shells, a discrete SPHARM transform is

performed at each value of r to obtain (3.5). Features derived from this representation, 78

however, do not provide a unique function representation [40, 41]. For instance, rotating

the inner and outer shells by different amount will result in different spatial distribution

of function values. However, in this approach, the derived features are insensitive to these

rotational transforms, thus resulting in the same feature values for dissimilar spatial

distributions.

drYdc lmmrl sin,,,

2

0 0

*

]2,...,3,2,1[ maxRr (3.17)

Burel and Henocq’s original equation (3.2) does not have this problem, since a part of the

basis function is a function of r. However, since (3.2) is computationally intractable [17],

we proposed an efficient approach that uses a radial transform (3.6), derived from (3.2),

to obtain a unique function representation. The transform (3.6) retains the relative

orientation information of the shells, thus the features derived will be sensitive to

independent rotations of the different shells, thereby ensuring that unique feature

representation is obtained.

mrl

R

r

mkl c

rkrrc sin2

max2

1

2

max2,...,3,2,1 Rk (3.18)

The range of k could be changed to obtain different lengths of the final feature vector.

However, to avoid unnecessarily increasing the feature vector length or losing any

79

important information caused by reducing the range, we choose to keep the range of k the

same as that of r, i.e. 2Rmax.

From the obtained representation (3.6), we then compute similarity transform invariant

features using (3.7) for each value of l and k [38] with p and q are used to index these

features. Note we reshape I into a single row vector of dimensions for later

analysis.

(3.19)

3.6 Authors' contributions

MJM conceptualized the study, supervised the collection of the data from UBC, and

supervised the application of the SPHARM technique to medical data. AU developed the

SPHARM-based method and performed the calculations. RA supervised the development

of the SPHARM-based method and assisted in the application to medical data. SP

collected the data at UBC and performed the manual segmentations of the thalami. ML

collected the data at UNC and manually segmented the data from UNC. XH supervised

the collection of UNC data and assisted in biological interpretation of the results.

3.7 Acknowledgements

This work was supported by a grant from NSERC/CIHR CHRP-(323602 - 06) (MJM).

80

3.8 References

[1] Bacci J-J, Kachidian P, Kerkerian-Le Goff L, Salin P: Intralaminar thalamic nuclei

lesions: widespread impact on dopamine denervation-mediated cellular defects in the rat

basal ganglia. Journal of Neuropathology and Experimental Neurology, 63(1):20-31,

2004

[2] Henderson JM, Carpenter K, Cartwright H, Halliday GM: Degeneration of the centre

median-parafascicular complex in Parkinson's disease. Annals of Neurology 2000,

47(3):345-352, 2000.

[3] Henderson JM, Carpenter K, Cartwright H, Halliday GM: Loss of thalamic

intralaminar nuclei in progressive supranuclear palsy and Parkinson's disease: clinical and

therapeutic implications. Brain 2000, 123(Pt 7):1410-1421, 2000.

[4] Halliday GM, Macdonald V, Henderson JM: A comparison of degeneration in motor

thalamus and cortex between progressive supranuclear palsy and Parkinson's disease.

Brain 2005, 128(Pt 10):2272-2280, 2005

[5] Aymerich MS, Barroso-Chinea P, Perez-Manso M, Munoz-Patino AM, Moreno-Igoa

M, Gonzalez-Hernandez T, Lanciego JL: Consequences of unilateral nigrostriatal

denervation on the thalamostriatal pathway in rats. European Journal of Neuroscience

2006, 23(8):2099-2108, 2006.

[6] Kerkerian-Le Goff L, Bacci J-J, Salin P, Aymerich MS, Barroso-Chinea P, Obeso JA,

Lanciego JL: Intralaminar Thalamic Nuclei are Main Regulators of Basal Ganglia:

81

Possible involvement in the pathophysiology of Parkinson's disease. In The Basal

Ganglia VIII. Edited by Bolam JP, Ingham CA, Magill PJ: Springer US;331-339, 2005.

[7] Nakamura Y, Otake K, Tokuno H: The parafascicular nucleus relays spinal inputs to

the striatum: an electron microscope study in the rat. Neuroscience Research 2006,

56(1):73-79, 2006

[8] Lacey CJ, Bolam JP, Magill PJ: Novel and distinct operational principles of

intralaminar thalamic neurons and their striatal projections. Journal of Neuroscience

2007, 27(16):4374-4384, 2007.

[9] Kimura M, Minamimoto T, Matsumoto N, Hori Y: Monitoring and switching of

cortico-basal ganglia loop functions by the thalamo-striatal system. Neuroscience

Research 2004, 48(4):355-360, 2004.

[10] Ogawa T, Yoshida Y, Okudera T, Noguchi K, Kado H, Uemura K: Secondary

thalamic degeneration after cerebral infarction in the middle cerebral artery distribution:

evaluation with MR imaging. Radiology 1997, 204(1):255-262, 1997.

[11] Tamura A, Tahira Y, Nagashima H, Kirino T, Gotoh O, Hojo S, Sano K: Thalamic

atrophy following cerebral infarction in the territory of the middle cerebral artery. Stroke

1991, 22(5):615-618, 1991.

[12] Hulshoff Pol HE, van der Flier WM, Schnack HG, Tulleken CA, Ramos LM, van

Ree JM, Kahn RS: Frontal lobe damage and thalamic volume changes. Neuroreport 2000,

11(13):3039-3041, 2000.

82

[13] Kassubek J, Juengling FD, Hellwig B, Spreer J, Lucking CH: Thalamic gray matter

changes in unilateral Parkinsonian resting tremor: a voxel-based morphometric analysis

of 3-dimensional magnetic resonance imaging. Neuroscience Letters 2002, 323(1):29-32,

2002.

[14] Summerfield C, Junque C, Tolosa E, Salgado-Pineda P, Gomez-Anson B, Marti MJ,

Pastor P, Ramirez-Ruiz B, Mercader J: Structural brain changes in Parkinson disease with

dementia: a voxel-based morphometry study. Archives of Neurology 2005, 62(2):281-

285, 2005.

[15] Kaasinen V, Maguire RP, Hundemer HP, Leenders KL: Corticostriatal covariance

patterns of 6-[18F] luoro-L-dopa and [18F] luorodeoxyglucose PET in Parkinson's

disease. Journal of Neurology 2006, 253(3):340-348, 2006.

[16] Bookstein FL: "Voxel-based morphometry" should not be used with imperfectly

registered images. Neuroimage 2001, 14(6):1454-1462, 2001.

[17] Ashburner J, Friston KJ: Why voxel-based morphometry should be used.[comment]

Neuroimage 2001, 14(6):1238-1243., 2001.

[18] Miller MI, Beg MF, Ceritoglu C, Stark C: Increasing the power of functional maps

of the medial temporal lobe by using large deformation diffeomorphic metric mapping.

Proceedings of the National Academy of Sciences of the United States of America 2005,

102(27):9685-9690, 2005.

83

[19] Stark CEL, Okado Y: Making memories without trying: medial temporal lobe

activity associated with incidental memory formation during recognition. Journal of

Neuroscience 2003, 23(17):6748-6753, 2003.

[20] Yushkevich PA, Detre JA, Mechanic-Hamilton D, Fernandez-Seara MA, Tang KZ,

Hoang A, Korczykowski M, Zhang H, Gee JC: Hippocampus-specific fMRI group

activation analysis using the continuous medial representation. Neuroimage 2007,

35(4):1516-1530, 2007.

[21] McKeown M, Li J, Huang X, Wang ZJ: Local Linear Discriminant Analysis

(LLDA) For Inference Of Multisubject fMRI Data. . In IEEE Acoustics, Speech and

Signal Processing: 2007; Honolulu, Hawaii; 2007:305 – 308, 2007.

[22] Mangin JF, Poupon F, Duchesnay E, Riviere D, Cachia A, Collins DL, Evans AC,

Regis J: Brain morphometry using 3D moment invariants. Medical Image Analysis 2004,

8(3):187-196, 2004

[23] Ng B, Abu-Gharbieh R, Huang X, McKeown MJ: Characterizing fMRI Activations

within Regions of Interest (ROIs) Using 3D Moment Invariants, . In Proceedings of

Conference on Computer Vision and Pattern Recognition: 2006; New York;

2006:63,2006

[24] Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ: Invariant SPHARM

Shape Descriptors for Complex Geometry in MR Region of Interest Analysis. In 29th

Annual International Conference IEEE EMBS: 2007; Lyon, France; 2007.

84

[25] Matthews MA: Death of the central neuron: an electron microscopic study of

thalamic retrograde degeneration following cortical ablation. Journal of Neurocytology

1973, 2(3):265-288, 1973

[26] Vicedomini JP, Corwin JV, Nonneman AJ: Role of residual anterior neocortex in

recovery from neonatal prefrontal lesions in the rat. Physiology & Behavior 1982,

28(5):797-806, 1982.

[27] Ross DT, Ebner FF: Thalamic retrograde degeneration following cortical injury: an

excitotoxic process? Neuroscience 1990, 35(3):525-550, 1990.

[28] Sorensen JC, Dalmau I, Zimmer J, Finsen B: Microglial reactions to retrograde

degeneration of tracer-identified thalamic neurons after frontal sensorimotor cortex

lesions in adult rats. Experimental Brain Research 1996, 112(2):203-212, 1996.

[29] Kumon Y, Sakaki S, Watanabe H, Nakano K, Ohta S, Matsuda S, Yoshimura H,

Sakanaka M: Ciliary neurotrophic factor attenuates spatial cognition impairment, cortical

infarction and thalamic degeneration in spontaneously hypertensive rats with focal

cerebral ischemia. Neuroscience Letters 1996, 206(2-3):141-144, 1996.

[30] Yamada K, Kinoshita A, Kohmura E, Sakaguchi T, Taguchi J, Kataoka K,

Hayakawa T: Basic fibroblast growth factor prevents thalamic degeneration after cortical

infarction. Journal of Cerebellar Blood Flow and Metabolism 1991, 11(3):472-478, 1991.

[31] Jackson GF, 3rd, Villablanca JR, Loopuijt LD: Few neocortial and thalamic

morphological changes after a neonatal frontal cortical ablation contrast with the effects

85

of a similar lesion in fetal cats. Brain Research 1995, Developmental Brain Research.

90(1-2):62-72.

[32] Villablanca JR, Burgess JW, Benedetti F: There is less thalamic degeneration in

neonatal-lesioned than in adult-lesioned cats after cerebral hemispherectomy. Brain

Research 1986, 368(2):211-225, 1986.

[33] Amini L, Soltanian-Zadeh H, Lucas C, Gity M: Automatic segmentation of thalamus

from brain MRI integrating fuzzy clustering and dynamic contours. IEEE Transactions on

Biomedical Engineering 2004, 51(5):800-811, 2004.

[34] Lewis M, Slagle C, Smith A, Truong Y, Bai P, McKeown M, Mailman R, Belger A,

Huang X: Task specific influences of Parkinson's disease on the striato-thalamo-cortical

and cerebello-thalamo-cortical motor circuitries. Neuroscience Letters 2007, 147(1):224-

235, 2007.

[35] Hoehn MM, Yahr MD: Parkinsonism: onset, progression and mortality. Neurology

1967, 17(5):427-442, 1967.

[36] Damasio H: Human Brain Anatomy in Computerized Images; 2005.

[37] Ludbrook J: Advantages of permutation (randomization) tests in clinical and

experimental pharmacology and physiology. Clinical and Experimental Pharmacology

and Physiology 1994, 21(9):673-686, 1994.

[38] Burel G, Henocq H: Three-dimensional invariants and their application to object

recognition. Signal Process 1995, 45(1):1-22, 1995.

86

[39] Healey DM, Jr., Rockmore DN, Moore SB: An FFT for the 2-sphere and

applications. In: 1996; 1996:1323-1326 vol. 1323, 1996.

[40] Vranic DV: An improvement of rotation invariant 3D shape descriptor based on

functions on concentric spheres. In IEEE International Conference on Image Processing:

2003; Barcelona; 2003:757-760, 2003.

[41] Kazhdan M, Funkhouser T, Rusinkiewicz S: Rotation invariant spherical harmonic

representation of 3D shape descriptors. In Proceedings of the 2003 Eurographics/ACM

SIGGRAPH symposium on Geometry processing. Aachen, Germany: Eurographics

Association; 2003.

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4 Detection and Analysis of Anatomical Shape Changes

in MRI (PD brain ventricles)3

4.1 Introduction

Magnetic resonance imaging (MRI) is increasingly recognized as a suitable modality for

studying the human brain anatomy in vivo. Improvements in both MRI scanner hardware

and acquisition sequences are yielding progressively higher resolution 3D images of

internal brain structures. One of the main benefits of this increased resolution is in the

study of structure of brain anatomy. Researchers use MR images to delineate specific

brain areas, like the thalamus, to observe structural changes either over time or across two

or more subject groups, e.g. patients with Parkinson’s disease (PD) and normal

volunteers. This process of delineating specific structures to perform targeted analysis is

termed region of interest (ROI) analysis. Progress in automated segmentation is

increasingly yielding robust and consistent results which are slowly replacing the manual

delineation process [1, 2]. However, current methods are suitable mainly to segment

regions with clear anatomical boundaries, like the ventricles [3].

Numerous methods have been proposed to quantify and analyze the ROIs. The simplest

and most common approach uses the overall volume within an ROI, e.g. Anstey et al

used the hippocampal volume to investigate changes observed in mild cognitive

3A version of this chapter will be submitted for publication. Uthama A, Abugharbieh R, Traboulsee A, McKeown M. J, “Invariant SPHARM Shape Descriptors for Complex Geometry in MR Region of Interest Analysis”

88

impairment (MCI) [4]. However, studies using volumetric measures do not reflect actual

shape changes that might be indicative of neurological change. Vetsa et al. used medial

representations to characterize the surface of the caudate and identify shape changes in

schizophrenia [5]. However, this approach requires accurate alignment of the ROIs across

different subjects for valid analysis and hence residual errors in mutual alignment could

adversely affect the final results. Alternate methods rely on obtaining descriptive feature

vectors which may reflect the structural information in an ROI. These features may be

invariant to rotations, translations and scale, thus enabling easy comparison across

different subjects. This eliminates the need for mutual alignment, saving time and

potential inconsistencies arising from registration errors. Zimring et al [6] used spherical

harmonic (SPHARM) based invariant indices to accurately estimate and study volume of

brain lesions, reducing the errors due to subject positioning. In an earlier work, we used

scale, rotation and translation invariant features derived using a SPHARM representation

of 3D ROIs to analyze shape changes in brain MRI data [7] and demonstrated the

advantages of using such an approach along with traditional volumetric analysis.

However, the parameterization technique used in our previous work did not allow for

shapes with non-convex topology. In this paper, we extend our method and propose new

enhanced SPHARM shape descriptors that are unique to any ROI. These features also

enable the characterization of complex shapes with complex topology, including those

with multiple disjoint parts. We validate our method on synthetic data and demonstrate

the effectiveness of the proposed technique even in the presence of inter-subject

variability and misalignment between subjects.

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Gerig et al [8] proposed using a SPHARM surface representation for shape of brain

structures like the ventricles to better understand neurodevelopment and

neurodegenerative changes. Their approach however requires explicit alignment of the

structures along with volume normalization and is valid only for structures with spherical

topology. The SPHARM features proposed here is not limited to spherical topology and

natively incorporates alignment and scale issues as part of its invariant nature. Further

studies [9, 10] have also shown the importance of ventricular shape and volume in

understanding neurological disorders. In this study, we analyze the shape of lateral

ventricles in population of subjects with Parkinson’s disease and detect significant

changes not detected by the conventional volumetric method.

4.2 Methods

In this section, we briefly summarize our earlier work on SPHARM-based ROI

descriptors in MRI. We then proceed to present the proposed enhancements used to

enable the study of complex ROI topologies including a novel radial transform used to

obtain unique features for any ROI.

4.2.1 Proposed Invariant SPHARM features

A 3D ROI with spherical topology can be expressed as ),( , a function defined on

the unit sphere with and as the zenithal and azimuthal angles respectively. The value

of the function at a given ( , ) is equal to the distance to the surface point from the

centroid at those angles [7]. The SPHARM representation of this function is given by:

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(4.20)

),(* lmY is the complex conjugate of the mth order spherical harmonic of degree l, where

l ranges from 0 to L [11]. The accuracy of this representation depends on the value of L,

also called the bandwidth.

Invariance of the representation to translation is obtained by shifting the origin of the

3D ROI to its centroid before computing the SPHARM coefficients. In our previous work

[7], we employed rotationally invariant features from this representation using (4.2).

Scale normalization was achieved by scaling the vector obtained in (4.2) with its first

element, which gives a rough measure of total volume [7].

(4.21)

Non convex topologies, i.e. surfaces with self occlusions, or topologies with disconnected

components cannot be represented as a function of two variables, ),( , since these

topologies do not always have a single distance value for all ( , ). A third variable r,

the distance from the origin can be introduced to extend the definition to include such

shapes. The augmented function ),,( r is then binary valued, taking a non-zero value

only in points inside the 3D ROI. The SPHARM representation of such a function is

given by:

(4.22)

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k is an index introduced to account for possible degeneracy [11]. Since direct

computation of (3) is highly inefficient, we use an alternate approach by representing the

data as a set of spherical functions. These functions are obtained by intersecting the 3D

binary ROI with R spherical shells of increasing radii r. This intersection is simulated by

sampling the 3D ROI on a spherical grid of constant dimensions 2L2L at each value of r

[12]. The SPHARM coefficients are then obtained at each value of r as:

(4.23)

This results in a SPHARM representation for each shell. Invariant features for these

shells can then be derived using (2), as used by Kazhdan et al [13]. However, as the

authors themselves note, this representation is not unique, since independent rotations of

the shape along any of the constituting shells will result in the same feature vector

representation even though the topologies of the shapes are drastically different. To

overcome this limitation, we propose adapting the radial transform in (4.3) across these

features as in (4.5). This yields unique features even under independent rotations along

the shells. To achieve scale invariance across different ROIs, we propose to keep the

number of shells, S, constant at 2Rmax for all ROIs being analyzed. Rmax is the radius

measure in voxels of the smallest common sphere encompassing each of the ROI in the

entire set being analyzed.

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(4.24)

Since this radial transform is applied across each value of r, as shown in (4.5), the vector

must be of the same length for each shell. Hence, we use a common value of L for all

shells, whose minimum value is obtained by equating the surface area of the

encompassing sphere to the equiangular sampling grid (4.6).

max2max ,224 RLLLR (4.25)

The final unique, scale, translation and rotation invariant features are defined as in (4.7).

These values are then reshaped into a single row to provide the final feature vector.

(4.26)

Figure 4.1 shows how this method could be used to analyze 3D ROIs like the human

brain ventricles.

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Figure 4.19 Intersection of a left brain ventricle with 2 of the 128 shells used to obtain the SPHARM representation. The corresponding sampled surfaces of the two shells are also

shown.

4.2.2 Statistical Analysis of Features

The feature vectors thus obtained are of a high dimension, dependent on the value of L

chosen. Moreover, the generating probabilities of these features are unknown. We thus

employ a non-parametric permutation test for the statistical analysis of these features,

since no assumptions of the feature parameters are required.

In permutation tests, a distance measure between two groups of shapes (represented by

their feature vectors) is tested against the distance obtained by all possible permutations

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of the vectors across the two groups. We use the Euclidian distance between the feature

vectors as the distance measure. Also, as reported by Vetsa et al [5] we use a Monte

Carlo approach to obtain a sufficiently high number of permutations, since testing against

all possible permutations is not feasible. A final p value is obtained as the ratio of the

number of permutations which yielded a Euclidian distance greater than the original

ordering of the samples and the total number of permutations performed. If the obtained p

value is less than a statistical standard threshold of 0.05, the two groups are declared to

have significant differences between them. In our study, this is a strong indication that the

shapes in the two groups have a systematic difference in structure.

4.2.3 Automated segmentation of the lateral ventricles

The segmentation of the lateral ventricles was obtained using the voxel-based

morphometry approach [14]. The ventricles were segmented in the subject space without

spatial normalization. The left and right ventricles were segmented on the tissue

probability map (TPM) of the cerebrospinal fluid. This TPM, along with those for white

and grey matter were registered to the T1 anatomical scan of each subject. These

registration parameters were then used to obtain the ventricles segmentation in the subject

brain space. Automatic 3D connectivity methods and morphological operators were then

used to trim the results of segmentation. Figure 4.1 shows the result of once such

segmentation.

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4.3 Data and Imaging

This section describes the generation and acquisition of data used to test our proposed

approach, which include synthetic validation data as well as real structural MRI data of

patients and controls.

4.3.1 Synthetic Structural Data Generation

To verify the performance of the proposed shape description technique, we test the

SPHARM features on synthetic data with simulated, but nevertheless realistic inter-

subject variability. Similar to [6], the basic shape used to generate these data is an

ellipsoid as defined in (4.8), where (xc, yc, zc) is the centroid with (a, b, cG) as parameters

defining the 3D volume of the ellipsoid (4.8). The advantage of such an experimental

setup is in ability to quantitatively control the shape of the object; this lets us gauge the

performance of SPHARM features with increasing noise and variability. Keeping the

equatorial radii, a and b constant, the polar radius cG can be systematically varied to

create shapes with simple differences. The ability of the SPHARM features in

discriminating two groups of ellipsoids generated with a small difference in their

respective polar radii can be used as a measure of its sensitivity.

(4.27)

To ensure that most sources of variations observed in real life are considered in this

experiment, each ellipsoid, generated in a 128×128×128 voxel grid, was put through

some pre-processing. First, to create a more realistic irregular surface seen in ROI masks,

uniformly distributed random noise was added to the generated ellipsoidal binary mask.

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This was followed by a 3D Gaussian smoothing with a 5×5×5 voxel kernel with a

standard deviation of 4. Finally, the result was converted back into a binary mask using a

threshold of 5. These values were obtained heuristically from the observation of real

ROIs of the thalami in normal subjects. To simulate the effects of intersubject variability

in both size and shape. All the three radii values were perturbed independently by up to

0.2 units, resulting in a maximum voxel count (volume) change of up to 25%. This

change is comparable to the variations observed in real data (Section IV-B). To simulate

the effects of subject position within the scanner, the centroid for each ellipsoid was

randomly perturbed by up to 5 voxels about the common origin fixed at the centre of the

voxel grid (64, 64, 64). Further, the ellipsoid was then rotated about a random

combination of x, y, and/or z axis by an angle generated from a uniform distribution

between 045˚.

Figure 4.20 (a) Surface rendering of a real left thalamus (top) and right thalamus (bottom) from a PD patient, note the rough edges. (b) Group A synthetic samples (see text)

generated with parameter set (2, 5, 10). (c) Group B synthetic sample generated with parameter set (2, 5, 8). Note the realistic looking edges in the synthetic data.

97

4.3.2 Real Structural MR Data Acquisition

The data used in this study consisted of MRI scans of 23 control subjects and 23 PD

patients. Two scans were performed with a gap of two hours, one before and one after the

administration of the drug L-dopa. The MR data were acquired on a 3.0 Tesla Siemens

scanner (Siemens, Erlangen, Germany) with a birdcage type standard quadrature head

coil and an advanced nuclear magnetic resonance echoplanar system. The participant’s

head was positioned along the canthomeatal line. Foam padding was used to limit head

motion within the coil. High-resolution T1 weighted anatomical images (3D SPGR,

TR=14ms, TE=7.7 ms, flip angle=25°, voxel dimensions 1.0×1.0×1.0mm, 176×256

voxels, 160 slices) were acquired.

4.4 Results and Discussion

This section presents quantitative results of employing the proposed SPHARM shape

features on the synthetic and real MR data outlined before.

4.4.1 Validation on Synthetic Data

Synthetic data generated as described earlier consisted of forty one data sets each set

having two groups, A and B, each group with twenty sample shapes. Group A was re-

generated independently each time with a baseline parameter set (2, 5, 10). Group B was

generated using a different baseline parameter, starting with (2, 5, 8) and ending with (2,

5, 12), with the value of cb being incremented by 0.1. The proposed SPHARM invariants

were then derived for all samples. Rmax was found to be 22; hence 44 shells were used to

parameterize the ROIs. A value of 40 was chosen for L as per (4.6), resulting in a feature

vector length of 1760 elements. The Euclidian distance between the SPHARM features of

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the two groups, A and B, was recorded. Permutation tests were then performed to

determine the level of significance in the difference between the features of the two

groups. Figure 3 summarizes the results of this analysis.

Figure 4.21 . Plot of the Euclidian distance between the two groups A and B for different values of cb, (ca was fixed at 10 for all points). Distances resulting in a significant

difference (alpha = 0.05) between the groups as obtained by the permutation test are indicated with a star. Non-Significant distances are indicated with a dot.

The graph in Figure 4.3 shows the expected trend in the Euclidian distance measure

between the two groups. For values of cb smaller than 9.5 and larger than 10.6, the

features are able to detect a systematic difference in shape between the two groups.

However, as the value of cb approaches 10 (the value of ca), there is less difference in the

sample shapes between the two groups. For values of cb in the range (9.5, 10.6), the

combined effect of the various perturbations in the parameters involved, coupled with the

inter-subject variability introduced, leaves almost no difference in constituting shapes of

99

the two groups. This is shown in Figure 3 with dots, indicating that the permutation test

was unable to find any systematic difference in the features vectors. This experiment

demonstrates the sensitivity of the proposed technique in discriminating subtle shape

changes between two groups.

4.4.2 Analysis of Real MR Structural Data

The proposed technique was next used to analyze the structure of the left and the right

ventricle in patients with Parkinson’s disease. Both ventricles were segmented using the

automated segmentation method from each scan. Since the subject was scanned twice

within a short duration, two independently segmented ROIs were available for each

ventricle in each subject. SPHARM features were computed for each of the ROI masks so

obtained. Rmax was found to be 64 voxels; hence 128 shells were used to parameterize the

ROIs. The bandwidth L was set at 114 as per (4.6), resulting in a feature vector length of

14592. Since two scans were performed for each subject, two feature vectors were

obtained for each ROI, for each subject. Also, since the duration between the scans was

less than two hours, no systematic structural changes were expected between these two

observations. The only changes expected were due to repositioning, manual tracing

inconsistencies and other imaging artifacts. To confirm this assumption, each subject

group (Patients and Controls) was further sub-divided into two categories: pre-drug and

post-drug. Permutation test results of the SPHARM feature vectors between these two

sub-groups are shown in Table 4.1. Results from the volumetric analysis are also shown.

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Table 4.6 Result of pre-drug vs. post-drug analysis

Subject group ROI SPHARM p value Volumetric p value

Controls Left Ventricle 0.9803 0.9563

Controls Right Ventricle 0.9610 0.9710

PD Left Ventricle 0.9838 0.9638

PD Right Ventricle 0.9800 0.9781

The results in Table 4.1 indicate that, as expected, there are no statistically significant

changes in the shape of the ventricle between the two scans. Having established this, the

two feature vectors from the two sessions were then averaged to generate a single feature

vector for each ROI for each subject. Direct averaging is valid since these features

represent the same shape. Changes due to rotation and translations are annulled by the

invariance property of the features. This averaging reduces any potential variability

introduced by the automatic segmentation and other noise sources, thereby increasing the

sensitivity of the features to actual shape changes. A permutation test on the averaged

features was then performed between the two subject groups. Results are indicated in

Table 4.2. Results from the volumetric analysis are also shown.

Table 4.7 Result of comparison between control subjects and PD patients. Values indicated with a * are statistically significant at an alpha value of 0.05.

ROI SPHARM p value Volumetric p value

Left Ventricle 0.0462* 0.2711

Right Ventricle 0.0090* 0.2837

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As the ventricles may increase in size as a result of brain atrophy (so called

"hydrocephalus ex vacuo"), it remains to be seen if different shape changes correspond to

different aspects of PD such as dementia.

4.5 Conclusions

We enhanced our earlier work generating invariant SPHARM features for 3D ROI

analysis in MR data by extending our characterization capability to ROIs with complex

topologies, including those with possible disconnections. We also proposed the use of a

novel radial transform to obtain unique feature. The proposed features were able to detect

subtle shape changes in synthetically created data with realistic inter-subject variations.

Given the fact that these measures can be obtained non-invasively and serially this

method provides another means by which clinicians may monitor progression of disease,

and possibly test whether or not a given treatment affects the rate of disease progression.

Hence, the use of the proposed method to explore shape changes of different brain

structures as a biomarker of disease progression warrants further study.

102

4.6 References

[1] J. S. Suri, S. Singh and L. Reden, "Computer Vision and Pattern Recognition

Techniques for 2-D and 3-D MR Cerebral Cortical Segmentation (Part I): A State-of-the-

Art Review," Pattern Analysis & Applications, vol. 5, pp. 46-76, 2002.

[2] J. S. Suri, S. Singh and L. Reden, "Fusion of Region and Boundary/Surface-Based

Computer Vision and Pattern Recognition Techniques for 2-D and 3-D MR Cerebral

Cortical Segmentation (Part-II): A State-of-the-Art Review," Pattern Analysis &

Applications, vol. 5, pp. 77-98, 2002.

[3] M. G. Linguraru, M. Ballester and N. Ayache, "Deformable Atlases for the

Segmentation of Internal Brain Nuclei in Magnetic Resonance Imaging," International

Journal of Computers, Communications & Control, vol. 2, pp. 26-36, 2007.

[4] K. J. Anstey and J. J. Maller, "The role of volumetric MRI in understanding mild

cognitive impairment and similar classifications," Aging Ment. Health., vol. 7, pp. 238-

250, Jul. 2003.

[5] Y. S. K. Vetsa, M. Styner, S. M. Pizer, J. A. Lieberman and G. E. -. Gerig, Caudate

Shape Discrimination in Schizophrenia using Template-Free Non-Parametric Tests. , vol.

2879, 2003, pp. 661-669.

[6] D. Goldberg-Zimring, A. Achiron, S. K. Warfield, C. R. G. Guttmann and H. Azhari,

"Application of spherical harmonics derived space rotation invariant indices to the

103

analysis of multiple sclerosis lesions' geometry by MRI," Magn. Reson. Imaging, vol. 22,

pp. 815-825, 7. 2004.

[7] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs. volume:

Invariant shape descriptors for 3D region of interest characterization in MRI," in ISBI,

2006, pp. 754-757.

[8] G. Gerig, M. Styner, D. Jones, D. Weinberger and J. Lieberman, "Shape analysis of

brain ventricles using SPHARM," in 2001, pp. 171-178.

[9] M. Styner, J. A. Lieberman, R. K. McClure, D. R. Weinberger, D. W. Jones and G.

Gerig, "Morphometric analysis of lateral ventricles in schizophrenia and healthy controls

regarding genetic and disease-specific factors," Proceedings of the National Academy of

Sciences, vol. 102, pp. 4872-4877, 2005.

[10] X. Huang, Y. Z. Lee, M. McKeown, G. Gerig, H. Gu, W. Lin, M. M. Lewis, S. Ford,

A. I. Tröster, D. R. Weinberger and M. Styner, "Asymmetrical ventricular enlargement in

Parkinson's disease," Movement Disorders, vol. 22, pp. 1657-1660, 2007.

[11] G. Burel and H. Henocq, "Three-dimensional invariants and their application to

object recognition," Signal Process, vol. 45, pp. 1-22, 1995.

[12] D. M. Healey Jr, D. N. Rockmore and S. B. Moore, "An FFT for the 2-sphere and

applications," in 1996, pp. 1323-1326 vol. 3.

104

[13] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, 23-25 June 2003, 2003, pp. 156-65.

[14] J. Ashburner and K. J. Friston, "Voxel-based morphometry-the methods,"

Neuroimage, vol. 11, pp. 805-821, 2000.

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5 Extending SPHARM Features to Functional Activation

Analysis in fMRI 4

5.1 Introduction

Functional magnetic resonance imaging (fMRI) is one of the most commonly used

modalities for human brain mapping. Medical researchers often use this non-invasive

imaging technology to investigate normal brain functions as well as the effects of

neurological disease such as Parkinson’s (PD) [1]. Typically, the functional response

obtained in an fMRI experiment is analyzed on a voxel-by-voxel basis with the resultant

activation statistics assembled into a statistical parameter map (SPM). The most common

approach in generating an SPM is based on the general linear model (GLM) [2].

A key challenge in functional neuroimaging is determining how to meaningfully combine

results across subjects with varying brain sizes, brain shapes, and possibly even disease-

induced brain shape changes. A typical approach is to register each subject’s brain to a

common atlas and compute the SPMs in the template space. A comparison of some of the

spatial normalization methods was presented by Crivello et al. [3]. However, current

spatial normalization methods may give an imperfect registration result [4], resulting in

signals from functionally distinct areas, especially small subcortical structures, to be

inappropriately combined [5]. Spatial normalization may therefore lead to poor sensitivity

4A version of this chapter will be submitted for publication. Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ, “3D Regional fMRI Activation Analysis Using SPHARM-Based Invariant Spatial Features and Intersubject Anatomical Variability Minimization”,

106

in the fMRI data analysis due to reduced functional overlap across subjects as was

observed by Stark and Okado [6]. Extensive spatial smoothing is often performed to

increase the functional overlap across possibly misaligned subjects, but this procedure

degrades the overall spatial resolution.

An alternative approach that was recently investigated is to align the subjects at the

region of interest (ROI) level, as opposed to whole brain normalization. Miller et al. [7]

extended the work of Stark and Okado [6] by utilizing large deformation diffeomorphic

metric mappings (LDDMM). Also, an approach that uses continuous medial

representations (cm-rep) of the ROIs has also been proposed [8]. However, these

approaches still rely on structural features in the higher resolution scans to deform the

functional maps into a common space. This inherently assumes a high level of

correspondence between the structural and functional neuroanatomy across subjects. In

the presence of brain pathologies like PD, which are known to induce compensatory

changes affecting, this assumption may become problematic.

To circumvent these potential problems associated with normalization, many researchers

employ direct ROI analysis without using any normalization [9]. This results in enhanced

sensitivity to detection of activation [10]. However, to date, most direct ROI analysis

methods ignore information encoded by the spatial distribution of the activation statistics

and instead use simpler measures such as mean voxel statistics or percentage of active

voxels within an ROI as features [9], which ignore information encoded by the spatial

distribution of the activation statistics.

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An attempt in incorporating spatial information has been proposed [11], where the sums

of activation statistics within spheres of increasing radii were considered. However, these

features have limited sensitivity to spatial patterns since they only capture changes in the

radial direction. Ng et al. [12] proposed an alternate approach employing three

dimensional moment invariant features (3DMI) which were shown to be more sensitive

than conventional mean voxel statistics and percentage of activated voxels based

approaches in detecting task-related activation differences. The fact that the 3DMI

approach detected significant task-dependent features (e.g. spatial variance) across non-

normalized brain images is noteworthy, as it implies that the spatial features are sensitive

to task-related effects and robust to inter-subject anatomical differences. Nevertheless in

its current form, the 3DMI method will have reduced sensitivity to task-related functional

changes if inter-subject anatomical variability is large, especially when analyzing older

subjects or subjects with neurodegenerative disease. Also, as the authors noted, higher

order 3DMI features are more susceptible to noise and hence limit the maximum number

of discriminative features that can be derived [12].

SPHARM-based methods have previously been proposed in the context of 3D shape

retrieval systems by Vranic et al [13] and Kazhdan et al [14]. Both authors proposed

obtaining invariant SPHARM features by intersecting 3D shapes with shells of growing

radii. This approach, however, could not detect independent rotations of a shape along the

shells, thereby resulting in a non-unique representation [14]. In [15], the use of invariant

SPHARM descriptors for analyzing anatomical structures (represented as binary 3D

shapes) in MR was proposed. However, the shape parameterization employed was limited

to convex topologies, which significantly limits its applicability. However, these

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approaches were proposed to analyze the geometrical shape of an ROI, but not the

intensity distributions of an ROI, such as the spatial activation patterns in fMRI data.

In [20], we proposed a radial transform adapted from [16] to address the limitations of

[13, 14]. This resulted in a novel SPHARM-based structural feature representation that is

unique to the ROI and can be applied to any arbitrarily complex shape. We then extend

this application of 3D SPHARM-based features to characterize spatial activation patterns

in fMRI data. Importantly, these proposed features are unique to the ROI and invariant to

similarity transformations, so alignment of brains (or ROIs) across subjects is not needed.

Our key contribution is a novel approach to account for the underlying structural

(anatomical) inter-subject variability based on subspace projection methods. We validate

our proposed technique on synthetic data and demonstrate improved sensitivity as

compared to the 3DMI technique. We also demonstrate the effectiveness of the proposed

method on real fMRI data by discriminating medication (L-dopa) induced differences in

activation patterns of Parkinson’s disease (PD) patients.

5.2 Methods

In this section we first describe our proposed invariant SPHARM-based spatial features.

We then present the PCA subspace approach for minimizing effects of structural ROI

variability on functional analysis. Finally, we describe the statistical analysis method used

to generate the results.

5.2.1 Invariant SPHARM-Based Spatial Features

Let be a function defined on the unit sphere with and as the zenithal and

azimuthal angles, respectively. The SPHARM representation for this function is given by 109

(4.1) where is the complex conjugate of the mth order spherical harmonic of

degree l. l ranges from 0 to L [16]. Increasing the value of L, also called the bandwidth,

improves the representation accuracy at the cost of higher computation time. Burel and

Henocq [16] also extended this definition to real valued 3D distributions (5.2),

where r is the distance from the origin to a given voxel. k is an index introduced to

account for possible degeneracy due to the additional dimension [16].

dYdc lmml sin,,

2

0 0

* (5.28)

0 0

*2

0

2 sin,,,sin2

drYr

krddrrc lmmkl

(5.29)

As explained later in this section, rotationally invariant features can be derived from this

spherical harmonic representation. In our application, we also need the features to be

invariant to any translation of the entire ROI in 3D space. To achieve this, we move the

origin of the function , to the centroid of , where is given

by (5.3).

(5.30)

Since direct computation of (5.2) is highly inefficient [17], we use an alternate approach

by representing the data as a set of spherical functions obtained by intersecting the 3D

data with spherical shells. Alternatively, for each value of r, can be visualized

as a spherical shell comprising the function values at a distance r from the origin. r can

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then be incremented in steps of t to encompass the entire ROI. If the initial representation

of the function is in the form of a cubic grid (regular isotropic voxels in our case),

volumetric interpolation is required to resample the ROI in the spherical coordinate

space.

When analyzing multiple subjects’ functions simultaneously (e.g. fMRI activation data

for an ROI across a subject group), we define the maximum radius, Rmax, as the minimum

radial distance in voxel count that encompasses all non-zero values of all subjects’

functions being analyzed. To represent the values from the cubic grid of all functions

with sufficient accuracy, 2Rmax shells are used. To achieve scale invariance, the shells

must be distributed evenly throughout the spatial extent of each function. Since the ROI

size across subjects is not uniform, shell spacing t must be adjusted for each subject

separately. This procedure ensures that each shell captures similar features from the 3D

function irrespective of its scale.

Surface sampling along each of these shells is performed on an equiangular spherical grid

of dimensions 2L×2L [17]. The common bandwidth L for all shells of all functions is

chosen to satisfy the sampling criterion for the largest shell in this set of functions,

namely the one with radius Rmax. The surface area for this shell represents the maximum

surface shell area that needs to be sampled by the equiangular grid; hence, any value of L

satisfying the required equiangular sampling (2L×2L) at this shell will be sufficient to

represent data from smaller radii shells. The minimum value for L is obtained by equating

the surface area of this largest shell to the equiangular sampling grid (5.4). Higher values

of L are not used, since the computation time will increase. Also, this will result in longer

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feature vectors, complicating the analysis. Furthermore, Burel and Henocq [16] noted that

when the represented object is a discrete array, higher values of l, resulting from a larger

L, may correspond to sampling noise. Recognizing that in applications pertaining to

discrimination, high accuracy in the SPHARM representation is not a necessity, we chose

to use the minimum value for L as that obtained by (5.4).

max2max ,224 RLLLR (5.31)

To obtain the SPHARM representation for all shells, a discrete SPHARM transform is

performed at each value of r to obtain (5.5). Features derived from this representation,

however, do not provide a unique function representation as discussed in [13] and [14].

For instance, rotating the inner and outer shells by different amount will result in different

spatial distribution of function values. However, in this approach, the derived features are

insensitive to these rotational transforms, thus resulting in the same feature values for

dissimilar spatial distributions.

drYdc lmmrl sin,,,

2

0 0

*

]2,...,3,2,1[ maxRr (5.32)

Burel and Henocq’s original equation (5.2) does not have this problem, since a part of the

basis function is a function of r. However, since (5.2) is computationally intractable [17],

we earlier proposed an efficient approach that uses a radial transform (5.6), derived from

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(5.2), to obtain a unique function representation [20]. The transform (5.6) retains the

relative orientation information of the shells, thus the features derived will be sensitive to

independent rotations of the different shells, thereby ensuring that unique feature

representation is obtained.

mrl

R

r

mkl c

rkrrc sin2

max2

1

2

max2,...,3,2,1 Rk (5.33)

The range of k could be changed to obtain different lengths of the final feature vector.

However, to avoid unnecessarily increasing the feature vector length or losing any

important information caused by reducing the range, we choose to keep the range of k the

same as that of r, i.e. 2Rmax.

From the obtained representation (5.6), we then compute similarity transform invariant

features using (5.7) for each value of l and k as outlined in [16]. p and q are used to index

these features. Note we reshape I into a single row vector of dimensions for

later analysis.

(5.34)

5.2.2 fMRI Analysis Using SPHARM Features

Features extracted from fMRI activation statistics are influenced by two factors. The first

factor, which is the one of interest, corresponds to the functional aspect of the data as

exhibited by the spatial pattern of the activation statistics within the ROI. The second 113

factor is the shape of the anatomically-defined ROIs. In functional studies, the structural

information reflects pure inter-subject variability, which adversely affects the primary

aim of the analysis, namely resolving actual functional pattern changes across subjects. In

this section, we propose a novel approach for fMRI ROI characterization that uses

SPHARM-based features described in the previous section in a manner that minimizes

the effects of the underlying structural (inter-subject) variability.

In our approach, invariant features describing the shape of an ROI, SPHARM-s, are first

computed without incorporating the fMRI activation statistics within the ROI (5.8). We

then compute invariant features comprising of both structural and functional information,

SPHARM-fs, as in (5.9), where txyz is the real valued activation statistic obtained at the

voxel position (x, y, z). The difference between SPHARM-s and SPHARM-fs is that

SPHARM-s contains only shape information, whereas SPHARM-fs contain both

structural and functional information. We note that variations in ROI shapes thus affect

both vectors, SPHARM-fs and SPHARM-s.

(5.35)

(5.36)

To quantify the effects of inter-subject structural variability, we first derive the SPHARM-

s features for all subjects for a given ROI. Let Is be a matrix whose ith row corresponds to

the SPHARM-s features of the ith subject. Each of these feature vectors will have a length

D as explained in section 5.2.1. We apply principal component analysis (PCA) on the

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pooled structural information (of all subjects) in Is to determine the projection directions

of maximal variance. Means of each column of Is are first removed. A singular value

decomposition of Is is then applied to obtain a D×D matrix V and a diagonal Λ, where the

columns of V (eigenvectors) {vj} represents the principal component directions, and the

diagonal elements of Λ {λj} (eigenvalues) represents the variance of the corresponding

eigenvector. V spans a linear subspace where the first several projection directions {vj}

reflect maximum variations in the row elements of Is. Since Is contains the pooled

structural information for all subjects, these directions correspond to maximum inter-

subject structural variations. For the data used in this study, we observed that the first d (3

to 4) components of V account for up to 98% of the inter-subject variation.

To mitigate inter-subject variability, we first define a new set of projections V’ (5.10) by

removing the first d components for V. The resulting subspace V’ thus represents the set

of projections minimally effected by the inter-subject variation in ROI shape observed in

the SPHARM-s features across both groups.

(5.37)

To minimize the effects of the structural variations on functional analysis, let Ifs be the

matrix obtained by deriving the SPHARM-fs features for all subjects. The columns of Ifs,

{fsj}, are first mean centered and then projected onto the linear subspace V’ (5.11).

(5.38)

We denote features resulting from this projection as SPHARM-f features. The obtained

SPHARM-f features are minimally affected by structural variations, and thus ensure that

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subtle functional pattern changes will not be obscured by structural inter-subject

variability. Thus, discriminability in detecting activation pattern differences is enhanced

as will be demonstrated in Section 5.4.1. This approach is similar to methods used in the

face recognition application, where weighted PCA subspaces reduce the sensitivity of

different facial expressions within the same subject [18].

We validate our approach in section 5.4.1 on synthetic data, and show that the proposed

SPHARM-f features are more sensitive to functional pattern changes. Results indicate that

for a given level of inter-subject structural variations, SPHARM-f features perform

remarkably well even under high levels of noise. We demonstrate the practical use of our

approach by analyzing the effects of drug on the functional activation patterns of PD

patients.

5.2.3 Statistical Group Analysis

To efficiently discriminate two groups of 3D fMRI distributions, we first derive

SPHARM-f features for each subject’s ROI as explained in section 5.2.2. Then, to

determine the level of statistical significance in the difference between the groups, we use

the non-parametric permutation test as reported by Vesta et al [19]. This approach uses

the mean Euclidian distance between the feature vectors of the two groups to compute a p

value. A p value below the statistical standard threshold of alpha=0.05 is considered as

an indication of significant difference existing between the classes. This test is well suited

for our long feature vectors whose generating probability distributions are not known.

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5.3 Data and Imaging

This section describes the synthetic fMRI data we generated to validate the proposed

fMRI spatial analysis technique. It also outlines the imaging procedure used to obtain real

fMRI data from PD patients.

5.3.1 Synthetic fMRI Data

To demonstrate the validity of the proposed spatial analysis method, synthetic fMRI data

sets were generated using ROIs obtained from real MR data with actual inter-subject

anatomical variability. Eighteen binary ROI masks of the right cerebellar hemisphere

were obtained during two MR sessions of nine PD patients (imaging details presented in

Section 5.3.2). The same subjects took part in the two sessions, which were an hour apart

hence no significant structural changes were expected between them. However, since the

ROIs were manually delineated twice, i.e. on each subject’s image data pair from the two

sessions, inter-scan variability in the delineated shape were also expected to be present.

These 18 ROIs were then randomly assigned to two groups, A and B (9 each) to create a

data set with realistic inter-subject variability in ROI structure (shape). To simulate

affects of subject positioning in the scanner, these ROIs were then randomly rotated up to

an angle of ten degrees about a random combination of the three spatial axes. In an

approach similar to that used in [11] we generated synthetic functional patterns within the

binary ROI masks resulting in 3D SPMs. Since the aim of this experiment is to

demonstrate the sensitivity of the proposed features in detecting functional patterns, we

create group A with no patterns (pure noise) and group B with a simple, known,

quantifiable pattern. This pattern, for group B ROIs, was created using two levels of

117

baseline activation; -delta and +delta were used as activation values depending on the

distance from the functional centroid. The functional centroid for each subject was

obtained by a random perturbation of the ROI centroid by up to three voxels in all three

spatial directions. This was to simulate possible inter-subject variability in the functional

centroid in real data. –delta valued voxels were generated up to a distance of 4 voxels

from the functional centroid while for distances greater than 4 voxels, +delta valued

voxels were used.

Considerable amount of research has gone into examining the noise model in the fMRI

time series, yet no clear noise model exists for the spatial domain in the final parameter

maps. Kontos and Megalooikonomou choose to use a probabilistic model to generate the

pattern, but they do not add additional noise to the data [11]. Here, we choose to

generalize all sources of noise to a Gaussian model. To quantify of the level of noise

when compared to the signal amplitude present, we use the contrast to noise ratio (CNR)

defined by (5.12).

(5.39)

The aggregation of these two groups of functional data thus created is termed a set.

Multiple such sets were created for the actual experiment as explained further in Section

5.1 by varying the delta value. It is important to note that creation of each set begins from

the random assignment of the ROI pool into the two groups; hence the sets would be

considerably different from each other.

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Figure 5.1 shows the cross section of a real fMRI volume taken from the right cerebellar

hemisphere of a PD patient (data details explained in Section 5.3.2). Figure 5.2 shows

some of the generated patterns in group B for different values of delta. Figure 5.3 shows

a cross section of the generated synthetic fMRI activation values for a sample from group

A. As explained earlier, group A samples do not have any patterns in their activation

values and represent only noise.

Figure 5.22 A cross section of fMRI activation statistics from the right cerebellar hemisphere of a real subject.

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Figure 5.23 A cross section of synthetic fMRI activation statistics for group B from different sets. A pattern consisting of two activation levels corrupted by noise is present, -delta values closer to the functional centre and +delta away from the centre. (a) and (c) represent extreme cases where the pattern present is visually discernible in the presence

of noise. (b) and (d) represent very low signal strengths but are still detected by the proposed features. The delta values correspond directly to those in Figure 5.4. A Gaussian noise source of zero mean and σ0 of one was used in the above figures.

Figure 5.24 A cross section of fMRI activation statistics for group A synthetic data. Note the absence of a pattern

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5.3.2 fMRI Data of PD Patients

fMRI data was collected from nine subjects with Parkinson’s disease after approval from

the appropriate ethics review boards. Subjects were tested in the morning after a 12-hour

overnight withdrawal of their medication. Two motor tasks in 20 second blocks were

performed with the right hand. In the first task, subjects were externally guided (EG)

using a finger tapping video. In the second internally guided (IG) task, subjects

performed a finger tapping sequence previously seen on a screen during the first task.

Subjects were then given a single 100/25 L-dopa/carbidopa tablet with a light snack, and

the entire experiment was repeated an hour later. Images were acquired on a 3.0 Tesla

Siemens scanner (Siemens, Erlangen, Germany). High-resolution T1-weighted

anatomical images were acquired for co-registration with the functional images. Co-

planar T2-weighted functional images were acquired at each time point using

TR=3000ms, TE=30ms, 3.0×3.0×3.0mm, 64×64 voxels, 49 slices. Data preprocessing

included correction for slice timing, motion correction, and smoothing using SPM 2 [2].

A t-test was then performed on each voxel time course based on the signal changes

between the two tasks and rest condition. Voxel-based activation statistics were then

assembled into an SPM. ROIs for the left and right cerebellar hemisphere, basal ganglia

and the caudate were manually drawn using IRIS 2000 (NeuroLib, University of North

Carolina) on the T1 scans by a trained technician.

5.4 Results and Discussion

This section presents the results of applying our proposed fMRI spatial analysis technique

on the synthetic and real data described in Section 5.3.

121

5.4.1 Validation on Synthetic Data

Synthetic data were generated in sets, as described in Section 5.3.1, with every set

containing two groups, A and B, with 9 ROIs each. fMRI activation patterns for group A

were regenerated for each set. For Group B, the value of delta was incrementally varied

before regeneration. A Gaussian with zero mean and σ0 of one was used as the noise

Figure 5.25 Results of the synthetic data experiment. The normalized Euclidian feature distance between groups A and B for each set is plotted against delta for the 3DMI,

SPHARM-fs and SPHARM-f features. The black diamond markers represent the distances which yielded significant difference using 3DMI features, the red triangles represent

SPHARM-fs features while the blue pentagrams represent SPHARM-f features. The closer the markers are to the zero delta mark, the smaller the failure range, hence better the performance. 3DMI has a failure range of (-1.5, 1.25), SPHARM-fs has a range (-1.1,

1.3), while SPHARM-f features return the best results by being able to discriminate the groups even at every low values of delta (-0.2, 0.7)

source. A total of 101 sets were generated with delta varying from -2.5 to +2.5 in steps of

0.05. The maximum radius of the entire ROI set was found to be 14, hence a bandwidth

of 26 was chosen as per (5.4). The feature vector length obtained was 728 for the

SPHARM-s and the SPHARM-fs features. After discarding 4 components in the PCA

space, the feature vector length of SPHARM-f features was 724. SPHARM-fs and

SPHARM-f features were then derived for each set along with 3DMI features (feature 122

length of 9) for comparison. The Euclidian distance between the group means of each of

these features were recorded at all values of delta while performing the permutation tests.

The plot in Figure 5.4 uses markers to indicate distances that resulted in the permutation

test detecting a statistically significant difference between Group A and Group B. As

delta approaches zero, there is reduced functional pattern change for the features to

detect. After a point (indicated by the vertical lines) functional patterns are no longer

detected resulting in loss of significance.

Large magnitudes of delta indicate large amounts of functional differences between the

two groups. For delta values less than 1.5 and greater than 1.3, enough functional

changes exist for all three methods (SPHARM-fs, SPHARM-f and 3DMI) to effectively

discriminate the two groups. As delta approaches zero, inter-subject variability begins to

dominate. Primary sources of this variability are anatomical structural variations between

subjects, functional centroid variations and the noise added. SPHARM-fs fails for delta

values between (1.1, 1.3), indicating a higher susceptibility to inter-subject variability.

3DMI features fail in the range of delta values between (1.5, 1.25). Both SPHARM-fs

and 3DMI failed at a few points outside this range, this could be attributed to various

noise sources involved and the nature of the permutation test used (false negatives).

Having accounted for most structural variations, SPHARM-f performs the best, failing

only at the smallest range of delta (0.2, 0.7). This clearly demonstrates that SPHARM-f

features are extremely effective in discriminating subtle functional changes even in the

presence of differences in ROI shapes and inter-subject variations in the functional

centroid. The primary objective of this synthetic experiment: to demonstrate that our

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method of accounting for structural inter-subject variability does in fact improve the

sensitivity of our proposed features was clearly demonstrated.

5.4.2 Application to Clinical fMRI Data of PD Patients

SPHARM-s, SPHARM-fs and SPHARM-f and 3DMI features were derived for the clinical

data outlined in Section 5.3.2. Table 5.1 summarizes the findings of our analysis with

these features. The two groups compared were ‘before drug’ and ‘after drug’. The

sampling bandwidth was determined using (5.4) with the maximum radius from each ROI

class separately, resulting in a feature vector length of 724 for the cerebellar hemisphere

and the caudate. The IG and the EG rows indicate functional (3DMI, SPHARM-fs and

SPHARM-f) results for internally and externally guided tasks respectively. None of the

groups showed significant differences when analyzed using 3DMI or SPHARM-fs

features, whereas SPHARM-f detected a difference in the right caudate.

The presence of a neurological disease like PD may result in atrophy of brain structures,

which increases the variations in ROI shape normally seen across subjects. This suggests

that utilizing our proposed SPHARM-f features would result in increased sensitivity to

activation changes when discriminating across groups. As shown in Table 5.1, using

SPHARM-s features we were able to show that there were no significant structural

differences between the two groups, implying that structural variations manifest entirely

as inter-subject variations. The results from SPHARM-f analysis indicate that medication

(L-dopa), as expected, causes a change in the activation seen in the right caudate nucleus

since lack of dopamine in this region is a key feature of Parkinson’s. No change in the

cerebellar hemisphere were observed, as expected, since this structure is not directly

124

implicated in the initial pathology and represents changes ‘further downstream’ in the

motor pathway.

Table 5.8 Permutation test results (p value) of fMRI data analysis from the Parkinson’s disease study (the two groups being ‘before drug’ and ‘after drug’). IG: Internally guided,

EG: Externally guided, L: Left, R: Right, CRB: Cerebellar hemisphere, CAU: Caudate. Numbers in bold are statistically significant (alpha = 0.05).

L CRB R CRB L CAU R CAU

IG (3DMI) 0.6806 0.3185 0.2176 0.5163

EG (3DMI) 0.7728 0.1198 0.2036 0.6045

IG (SPHARM-fs) 0.1141 0.2746 0.2717 0.4516

EG (SPHARM-fs) 0.1466 0.1066 0.2160 0.3160

IG (SPHARM-f) 0.0600 0.3600 0.6233 0.2897

EG (SPHARM-f) 0.5097 0.4995 0.2739 0.0301*

5.5 Conclusions

In this paper, we proposed a new technique for analyzing spatial activation patterns in

fMRI data using 3D SPHARM features. These features were obtained by intersecting 3D

data distributions with concentric shells of increasing radii followed by a radial

transform. This radial transform addressed previous limitations of ROI representations

having non-unique feature vectors. Our main contribution was a novel approach to

discriminate subtle changes in spatial distribution within a 3D ROI by accounting for

anatomical (structural) shape variations across subjects. The effectiveness of the proposed

approach in mitigating structural variability was validated on synthetic data. We also

applied this approach to discriminate functional pattern changes within anatomical ROIs

in fMRI data collected from Parkinson’s’ disease patients associated with drug (L-Dopa)

administration.

125

An interesting application of this approach would be to compare activation patterns

between two subject groups that are expected to have systematic changes in both

structural and functional aspects. Avenues to decouple these aspects in the feature domain

would yield promising new directions in fMRI data analysis.

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5.6 References

[1] S. T. Grafton, "Contributions of functional imaging to understanding parkinsonian

symptoms,” Current Opinion in Neurobiology. vol. 14, pp. 715-719, Dec. 2004.

[2] K. J. Friston, A. P. Holmes, K. J. Worsley, J. B. Poline, C. Frith and R. S. J.

Frackowiak, "Statistical Parametric Maps in Functional Imaging: A General Linear

Approach," Human Brain Mapping, vol. 2, pp. 189-210, 1995.

[3] F. Crivello, T. Schormann, N. Tzourio-Mazoyer, P. E. Roland, K. Zilles and B. M.

Mazoyer, "Comparison of spatial normalization procedures and their impact on

functional maps," Human Brain Mapping. (USA), vol. 16, pp. 228, 2002.

[4] O. T. Carmichael, H. A. Aizenstein, S. W. Davis, J. T. Becker, P. M. Thompson, C.

C. Meltzer and Y. Liu, "Atlas-based hippocampus segmentation in Alzheimer's disease

and mild cognitive impairment," Neuroimage, vol. 27, pp. 979-990, 2005.

[5] M. Ozcan, U. Baumgartner, G. Vucurevic, P. Stoeter and R. Treede, "Spatial

resolution of fMRI in the human parasylvian cortex: Comparison of somatosensory and

auditory activation," Neuroimage, vol. 25, pp. 877-887, 4/15. 2005.

[6] C. E. Stark and Y. Okado, "Making memories without trying: medial temporal lobe

activity associated with incidental memory formation during recognition," Journal of

Neuroscience., vol. 23, pp. 6748-6753, Jul 30. 2003.

[7] M. I. Miller, M. F. Beg, C. Ceritoglu and C. Stark, "Increasing the power of

functional maps of the medial temporal lobe by using large deformation diffeomorphic

127

metric mapping," Proceedings of the National Academy of Science U. S. A., vol. 102,

pp. 9685-9690, Jul 5. 2005.

[8] P. A. Yushkevich, J. A. Detre, D. Mechanic-Hamilton, M. A. Fernandez-Seara, K. Z.

Tang, A. Hoang, M. Korczykowski, H. Zhang and J. C. Gee, "Hippocampus-specific

fMRI group activation analysis using the continuous medial representation,"

Neuroimage, vol. 35, pp. 1516-1530, May 1. 2007.

[9] R. T. Constable, P. Skudlarski, E. Mencl, K. R. Pugh, R. K. Fulbright, C. Lacadie, S.

E. Shaywitz and B. A. Shaywitz, "Quantifying and Comparing Region-of-Interest

Activation Patterns in Functional Brain MR Imaging: Methodology Considerations,"

Magnetic Resonance Imaging, vol. 16, pp. 289-300, 4. 1998.

[10] A. Nieto-Castanon, S. S. Ghosh, J. A. Tourville and F. H. Guenther, "Region of

interest based analysis of functional imaging data," Neuroimage, vol. 19, pp. 1303-1316,

2003.

[11] D. Kontos and V. Megalooikonomou, "Fast and effective characterization for

classification and similarity searches of 2D and 3D spatial region data," Pattern

Recognition, vol. 38, pp. 1831-1846, 11. 2005.

[12] B. Ng, R. Abugharbieh, X. Huang and M. J. McKeown, "Characterizing fMRI

activations within regions of interest(ROIs) using 3D moment invariants," in MMBIA,

2006.

[13] D. V. Vranic, "An improvement of rotation invariant 3D-shape based on functions

on concentric spheres," , ICIP pp. III-757-60 vol.2, 2003.

128

[14] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, 23-25 June 2003, 2003, pp. 156-65.

[15] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs.

volume: Invariant shape descriptors for 3D region of interest characterization in MRI," in

ISBI, pp. 754-757, 2006

[16] G. Burel and H. Henocq, "Three-dimensional invariants and their application to

object recognition," Signal Processing, vol. 45, pp. 1-22, 1995.

[17] D. M. Healey Jr, D. N. Rockmore and S. B. Moore, "An FFT for the 2-sphere and

applications," ICASSP, pp. 1323-1326 vol. 3, 1996

[18] Y. Zhang and A. M. Martinez, "Recognition of expression variant faces using

weighted subspaces," in Proceedings of the 17th International Conference on Pattern

Recognition, ICPR 2004, pp. 149-152, 2004.

[19] Y. S. K. Vetsa, M. Styner, S. M. Pizer, J. A. Lieberman and G. E. -. Gerig, Caudate

Shape Discrimination in Schizophrenia using Template-Free Non-Parametric Tests. ,

MICCAI, vol. 2879, pp. 661-669, 2003.

[20] A. Uthama, R. Abhugharbieh, A. Traboulsee and M. J. McKeown, "Invariant

SPHARM shape descriptors for complex geometry MR region of interest analysis in MR

region of interest analysis," Engineering in Medicine and Biology, pp. 1322-1325, 2007

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6 Validation and Comparisons to Conventional fMRI

Analysis Approach 5

6.1 Introduction

Typically, the functional response obtained in an fMRI experiment is analyzed on a

voxel-by-voxel basis with the resultant activation statistics assembled into a statistical

parameter map (SPM). The most common approach in generating an SPM is based on the

general linear model (GLM) [1].

A key challenge in functional neuroimaging is determining a meaningful way to combine

results across subjects with varying brain sizes, shapes, and possibly even disease-

induced brain shape changes. A common approach is to warp each subject’s brain to a

common atlas, thereby normalizing it, and obtain SPMs in the template space. A

comparison of some of the spatial normalization methods was presented by Crivello et al .

[2]. However, current spatial normalization methods may give an imperfect registration

result [3], resulting in signals from functionally distinct areas, especially small subcortical

structures, to be inappropriately combined [4]. Spatial normalization may therefore lead

to poor sensitivity in the fMRI data analysis due to reduced functional overlap across

subjects, as observed by Stark and Okado [5]. Extensive spatial smoothing is often

performed to increase the functional overlap across possibly misaligned subjects,

5A version of this chapter is being prepared for publication. Ashish Uthama, Rafeef Abugharbieh, Samantha J. Palmer, Anthony Traboulsee and Martin J. McKeown, “Characterizing fMRI Activations in ROIs while Minimizing Effects of Intersubject Anatomical Variability”

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potentially degrading the overall spatial resolution [6]. Thirion et al [7] proposed an

interesting alternative based on belief propagation and the use of segmentation on

parameter maps to obtain ROIs. This approach is suited to whole brain analysis and might

not be readily adapted to functional analysis within specific ROIs, as is our interest here.

Also, if a single activation focus existed in the functional data, any shift in its location

with different tasks might go unnoticed if ROIs obtained from segmentation of functional

data were used. Here, we are interested in studying the effect of PD on specific brain

regions and hence prefer to guide the functional analysis with ROIs based on anatomical

data.

An alternate approach recently proposed for combining fMRI activation across subjects is

to align subjects at the region of interest (ROI), as opposed to the whole brain level.

Miller et al. [8] extended the work of Stark and Okado [5] by utilizing large deformation

diffeomorphic metric mappings (LDDMM). Also, an approach that uses continuous

medial representations (cm-rep) of the ROIs has been proposed [9]. However, these

approaches rely on manually-placed landmarks in the higher resolution scans to deform

the functional maps into a common space.

To circumvent these potential problems associated with normalization, many researchers

employ feature based ROI analysis without using any normalization [10]. This may result

in enhanced sensitivity in activation detection [11]. However, these methods ignore

information encoded by the spatial distribution of the activation statistics within an ROI

and instead use simpler measures such as mean voxel statistics or percentage of active

voxels within an ROI as features [10].

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Previous work has demonstrated the importance of incorporating spatial information

when determining if a ROI is considered modulated by behavioral task performance. One

such method uses sums of activation statistics within spheres of increasing radii [12].

However these features have limited sensitivity to spatial patterns since they only capture

changes in the radial direction. A more sensitive approach proposed by Ng et al. [13]

employs three dimensional moment invariant features (3DMI) of activation maps,

resulting in a more sensitive means of detecting task related activity than conventional

approaches that examine the mean ROI time course or determine the fraction of voxels

that are deemed active above a pre-specified threshold. An interesting result of Ng's

approach is that some features (e.g. spatial variance) are sensitive to task yet relatively

well invariant across subjects. However, this method does not directly account for

intersubject variability present in the ROI masks or its effect on the analysis. Also, as the

authors note, higher order 3DMI features are more susceptible to noise and hence limit

the maximum number of discriminative features that can be derived [13].

SPHARM-based methods have previously been proposed in the context of 3D shape

retrieval systems by Vranic et al [14] and Kazhdan et al [15]. Both authors proposed

obtaining invariant SPHARM features by intersecting 3D shapes with shells of growing

radii. This approach, however, could not detect independent rotations of a shape along the

shells, thereby resulting in a non-unique representation [15]. In [16], the use of invariant

SPHARM descriptors for analyzing anatomical structures (represented as binary 3D

shapes) in MR was proposed. However, the shape parameterization employed was limited

to convex topologies, which significantly limited its applicability. Most importantly, the

three SPHARM-based approaches described above were used to analyze the geometrical

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shape of an ROI surface, not the intensity distributions of an ROI volume, such as the

spatial activation patterns in fMRI data.

In order to prevent the non-unique characteristics of previous SPHARM-based

representations [14, 15], we have recently proposed a unique radial transform [17]. This

resulted in a novel SPHARM-based structural feature representation that is unique to an

ROI and can be applied to any arbitrarily complex shape. One contribution of the current

work is that we extend the unique SPHARM-based representation to characterize not just

the shape of an ROI, but the full 3D, non-spatially smoothed, spatial fMRI activation

pattern within an ROI. Each ROI-based feature is unique, allowing discrimination based

on the spatial characteristics of the activation within an ROI as a whole, and invariant to

similarity transformations, so mutual alignment of subject brains (or ROIs) is not needed.

Another contribution of the proposed approach is a novel way to account for the

underlying structural (anatomical) inter-subject variability in the ROI binary masks based

on subspace projection methods. We validate our proposed technique on synthetic data

and demonstrate improved sensitivity. We also demonstrate favorable performance

compared to other proposed ROI-based methods that do not require the specification of

additional landmarks [5].

We also demonstrate the effectiveness of the proposed method on real fMRI data. In

addition to the regions detected by traditional methods, the SPHARM based approach

detected additional task based activation differences in a bulb squeezing task performed

by normal subjects and PD patients.

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6.2 Methods

In this section we first describe our proposed SPHARM-based invariant spatial features.

We then present the principal component subspace approach for minimizing effects of

structural ROI variability on the functional analysis. The statistical analysis method used

to generate the results is then presented. Finally, we present the ROI normalization

approach we used for comparison.

6.2.1 Invariant SPHARM-Based Spatial Features

A 3D object can be described by a function in the Cartesian coordinate system.

This function could be binary valued, like an ROI binary mask (6.1), or real valued like

fMRI activation statistics within an ROI (6.2). txyz is the real valued activation statistic

obtained at the voxel position (x, y, z).

(6.40)

(6.41)

These functions can also be represented in the spherical coordinate system as ,

where r is the distance from the origin, is the zenithal angle and is the azimuthal

angle. Burel and Henocq proposed using the spherical harmonic expansion of such a

function (6.3) to obtain rotationally invariant features [18]. in (6.3) are the

complex conjugate of the mth order spherical harmonic basis functions of degree l. l

ranges from 0 to L, the bandwidth.

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0 0

*2

0

2 sin,,,sin2

drYr

krddrrc lmmkl

(6.42)

Direct computation of (6.3) to characterize 3D functions is highly inefficient [19] and has

thus not been used in a practical application. In [17] we proposed an alternate approach to

compute this representation using concentric spherical shells. By representing the data as

a set of spherical functions obtained by intersecting the 3D data with concentric shells of

unit voxel thickness, we were able to simplify (6.3) into (6.4) and (6.5) (where r and k

enumerate the shell numbers). This process is depicted in Figure 6.1. This representation

enables us to use a more computationally efficient transform described by Healey et al

[19], thus making SPHARM based features practical.

mrl

R

r

mkl c

rkrrc sin2

max2

1

2

(6.43)

drYdc lmmrl sin,,,

2

0 0

*

(6.44)

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Figure 6.26 Representing data as a set of spherical functions. Real fMRI data from the right cerebellar hemisphere of a normal subject performing the maximum frequency task (Section III-B) is shown (t>2 for clarity). The shells were obtained using a bandwidth of L=128. The physical values of both angles are non-uniformly spaced (Chebyshev nodes)

[19]. The threshold, bandwidth and the depicted transparent ROI boundary are for illustration purposes only.

The origin of these spherical shells is placed at the centre of mass of the 3D function. The

centre of mass is computed using the corresponding binary extent function (6.6). This

results in the SPHARM representation being invariant to translational effects, while

ensuring that the defined origins of and always overlap.

(6.45)

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Smax in (6.4) and (6.5) is the number of spherical shells used. To enable a scale invariant

representation across a set of 3D functions, a common number of shells, Smax, have to be

evenly spaced within the extent of each individual function separately. This has a similar

effect as scaling all functions volumetrically to fit inside a unit radius sphere, but without

the associated cost of resampling. For a cubic voxel grid, the spacing between the shells

has to be at maximum, 0.5 voxels wide, to enable fair sampling of all voxels. Given these

restrictions, we first find the 3D function with the largest extent (6.6) as measured by the

radius from the origin to the outer most non-zero point of the function. We term this

value of the radius (measured in terms of voxels) Rmax. To ensure that the spacing

constraint is met for all functions, Smax is then set using (6.7).

(6.46)

Surface sampling along each of these shells is performed on an equiangular spherical grid

of dimensions 2L×2L [19], where L is the bandwidth of the function (Healy et al use the

notation B to denote the bandwidth). This common bandwidth L for all shells of all

functions is chosen to satisfy the sampling criterion for the largest shell, namely the one

with radius Rmax. The exact spatial frequency of the functions on these shells is difficult to

quantify, therefore an accurate estimate of the bandwidth is not possible. Recognizing

that in applications pertaining to discrimination, high accuracy in the SPHARM

representation is not a necessity, we use a heuristic approach based on the surface area to

determine an adequate bandwidth. The surface area for the largest shell represents the

maximum surface shell area (in terms of voxels) that the sampling grid needs to span;

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hence the minimum value for L is obtained by equating the surface area of this largest

shell to the equiangular sampling grid (6.8).

max2max ,224 RLLLR (6.47)

Earlier work on SPHARM features using shells like these [14] [15] obtained invariant

shape features directly from (6.5). As explained by Kazhdan et al [15], this representation

is not unique. For instance, rotating any two shells by different amounts will result in a

different spatial distribution of function values. However their features were insensitive

to these rotational transforms, thus resulting in same feature vectors for dissimilar spatial

distributions. To circumvent this problem, we incorporate (6.4) into our SPHARM

representation [17]. Since this transform (6.4) operates along the radius, it retains the

relative orientation information of the shells. Thus, the features derived are sensitive to

independent rotations of different shells, ensuring that a unique feature representation is

always obtained.

From the SPHARM representation (6.4) so obtained, we compute rotationally invariant

features using (6.9) as outlined in [18]. h and i are used to index these features. Note that

we reshape I into a single row vector, termed the feature vector, of dimensions

for later analysis.

(6.48)

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6.2.2 fMRI Group Analysis Using SPHARM Features

Let and be the binary 3D ROI mask and fMRI statistics inside the

corresponding mask for the i’th subject of the j’th group. When multiple ROIs are

present, group analysis of each region is performed independently. SPHARM feature

vectors defined in section 6.2.1 (6.9) are derived for each of these functions using an Rmax

value obtained considering all subjects. This ensures that all feature vectors obtained are

of the same size D and are in the same scale, translation and rotationally invariant feature

space.

Let the matrix be the collection of SPHARM features (6.9) obtained from all

for group j. These features are termed SPHARM-s (structural) since they capture only the

structural aspects of the ROI. In this context, we emphasize that the term structure is used

to describe the information contained in the binary ROI masks of the subjects. Let the

matrix be the collection of SPHARM features (6.9) obtained from all for group

j. We term these features SPHARM-fs (function + structure). These features are

influenced by two factors. The first factor, which is the one of interest, is the functional

aspect exhibited by the spatial pattern of the activation statistics within the ROI. The

second factor is the shape of the anatomically-defined ROIs. In functional studies this

structural information reflects inter-subject variability, which adversely affects the

primary aim of the analysis: resolving functional pattern changes across subject groups.

Let and be the pooled SPHARM-s and SPHARM-fs feature vector matrices,

respectively, from all groups. A principal component analysis (PCA) of the pooled

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structural information in will determine directions of maximal structural variance. After

the means of each column of are removed, a singular value decomposition of yields

a D×D matrix V and a diagonal matrix Λ. The columns of V (eigenvectors) {vj} represent

the principal component directions, while the diagonal elements of Λ {λj} (eigenvalues)

represent the variance of the corresponding eigenvector. The directions of the

eigenvectors with larger magnitude of eigenvalues correspond to projections with

maximum inter-subject structural variations. We now define d as the number of

eigenvectors required to represent at least 95% of the total variance observed in .

To mitigate the effects of inter-subject variability observed in the binary ROI masks, we

first define a new set of projections V’ (6.10) by removing the first d components from V.

The resulting subspace V’ thus represents the set of projections minimally effected by the

inter-subject variation in ROI shape observed in the SPHARM-s features across both

groups.

(6.49)

Let be the mean centered collection of SPHARM-fs features from all groups. The

linear projection of this on the reduced subspace V’ is now obtained (6.11).

(6.50)

We denote features resulting from this projection as SPHARM-f features. The obtained

SPHARM-f features are minimally affected by structural variations, and thus ensure that

subtle functional pattern changes will not be obscured by structural inter-subject

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variability. The pooled approach described ensures that there is no systematic bias

introduced into the analysis. A similar method was used in a face recognition application,

where weighted PCA subspaces were used to reduce effects of different facial

expressions within the same subject [20].

We validate our approach in section IV on synthetic data, and show that the proposed

SPHARM-f features are more sensitive to functional pattern changes. Results indicate that

SPHARM-f features perform better than SPHARM-fs features indicating a positive effect

of mitigating the effects of structural variations. We demonstrate the practical use of our

approach by analyzing the effects of task speed on functional activation patterns of PD

patients and normal subjects.

6.2.3 Statistical Group Analysis

To efficiently discriminate two groups of 3D fMRI distributions, we first derive

SPHARM-f features for each subject’s ROI as explained in section 6.2.1. To determine

the level of statistical significance in the difference between the groups, we employ a

non-parametric permutation test as explained by Vesta et al [21]. Permutation tests

generate the null distribution of a hypothesis from the data itself and hence do not need a

prior assumption of its parameters. This makes it well suited for the analysis of long

feature vectors whose generating probability distributions are not easily definable.

We first separate (6.11) into the constituting groups , with representing the mean

feature vector for each group j. The features from are then randomly distributed into j

groups N times. Let represent the mean feature vector of the group j at the nth

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instance of this random permutation procedure. Usually j= {a,b}, since researchers are

most often trying to discriminate two groups (Control subjects vs. Patients, Task 1 vs.

Task 2, etc.). The distance between any two mean feature vectors is defined using the

Euclidean measure (12). q in (12) is an index into the elements of the feature vector.

(6.51)

The p value is computed based on the number of times the random permutation yields a

Euclidean distance greater than the initially observed distance (6.13).

(6.52)

A p value below the statistical standard threshold of is considered as an

indication that significant difference exists between the groups being analyzed. This

procedure can also be applied to the SPHARM-fs feature vectors in .

6.2.4 ROI Normalization Approach (ROI-N)

To demonstrate practical advantages of the discriminatory powers of the proposed

approach, we compare results with those obtained from spatial normalization of the ROIs.

We use an improved version of the ROI-AL method first proposed by Stark and Okada

[5]. The ROI normalization approach, ROI-N, proceeds by first obtaining the anatomical

T1 signal scan data for each of the subject ROIs. These anatomical ROIs are then rigid

registered to the first subjects anatomical ROI and averaged to obtain the group template

[5]. A non-linear spatial normalization approach [22] is then used to obtain the

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parameters required to warp each subjects anatomical T1 signal ROI to this template.

These parameters are then used to normalize the activation statistics inside the ROI to the

common template space. The results of each step were visually inspected to rule out any

gross failures by the registration or the normalization process.

Based on the assumption that the voxels now line up across subjects and groups, a final

test for difference in means across groups is performed at each voxel location yielding a

group level t-statistic map. A height threshold is then applied to retain only those voxels

that have significantly different means between the two groups. We then apply a cluster

size threshold [23]. Existence of at least one surviving cluster after these thresholding is

taken as an indication that the groups being analyzed have a significant difference

between them.

6.3 Data and Imaging

This section describes the synthetic fMRI data we generated to validate the proposed

fMRI SPHARM analysis technique. It then outlines the imaging procedure used to obtain

real fMRI data from PD patients and control subjects.

6.3.1 Synthetic fMRI Data

To demonstrate the validity of the proposed method, synthetic fMRI data sets were

generated using binary ROI masks obtained from real MR data. This ensures that our

synthetic examples have real world structural variability and also pose variability due to

positioning in the scanner. Ten binary ROI masks of the right cerebellar hemisphere were

obtained from the control subject group of our fMRI study. Let the set of these masks be

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denoted by . Synthetic fMRI activation statistics can then be injected into these

ROIs to obtain the corresponding set . Rmax for these sets was found to be 19

voxels, corresponding to 57mm at 3mm voxel resolution.

Spatial activation noise for each element of is generated independently from

normally distributed values with zero mean and unit variance. To mimic the intrinsic

spatial correlation of fMRI data, the values are spatially smoothed using a Gaussian

kernel (FWHM = 3.5mm) [7]. Depending on the experimental setup, a synthetic pattern

can then be added if required. The presence of activation is modeled after the examples

used by Kontos and Megalooikonomou [12]. To obtain a functional centroid for the

synthetic pattern, the centroid of each binary mask in is randomly jittered by up to

three voxels in all three spatial directions. This corresponds to a maximum displacement

of 12.7mm at a resolution of 3mm×3mm×3mm per voxel. A synthetic pattern can be

generated by setting all voxels within a distance of 5 voxels from the chosen centroid to a

value delta. While voxels at a distance between 5 to 10 voxels are set to –delta. This

magnitude of delta can be varied to obtain the desired SNR. This pattern is smoothed

using a Gaussian kernel (FWHM = 3.5mm) before adding the independently generated

noise to obtain the final set, . A cross section of one such element of is

shown in Fig 2. Note the close correspondence with real data shown alongside.

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Figure 6.27 (a) Cross section of a synthetic pattern injected into the binary mask of a real right cerebellar hemisphere. SNR = 1.204 dB. (b) Cross section of a real fMRI activation

statistic map mapped to the same color map

6.3.2 Real fMRI Data

This study was approved by the University of British Columbia Ethics Board. 10

volunteers with clinically diagnosed PD participated in the study. 10 healthy, age-

matched control subjects without active neurological disorders were also recruited.

6.3.2.1 Experimental Design

Subjects lay on their back in the functional magnetic resonance scanner viewing a

computer screen via a projection-mirror system. All subjects used an in-house designed

response device in their right hand, a custom-built MR-compatible rubber squeeze-bulb

connected to a pressure transducer outside the scanner room. They lay with their forearm

resting down in a stable position, and were instructed to squeeze the bulb using an

isometric hand grip and to keep their grip constant throughout the study. Each subject had

their maximum voluntary contraction (MVC) measured at the start of the experiment and

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all subsequent movements were scaled to this, they had to squeeze at 5-15% of MVC to

accomplish the task.

Using the squeeze bulb, subjects were required to control the width of an “inflatable ring”

(shown as a black horizontal bar on the screen) in order to keep the ring within an

undulating pathway without scraping the sides. The pathway used a block design with

sinusoidal sections in two different frequencies (0.25 and 0.75 Hz) in a pseudo-random

order, and straight parts in between where the subjects had to keep a constant force of

10% of MVC. The frequencies were chosen based on prior findings and pilot studies

were used to determine that PD subjects could comfortably perform the required task.

Each block lasted 20 seconds (exactly 10 TR intervals), alternating a sinusoid, constant

force, sinusoid and so on to a total of 4 minutes. Before the first scanning session,

subjects practiced the task at each frequency until errors stabilized and they were familiar

with the task requirements.

Custom Matlab software (The Mathworks, Natick, MA) and the Psychtoolbox [24] was

used to design, present stimuli, and to collect behavioral data from the response devices.

6.3.2.2 Data Acquisition

Functional MRI was conducted on a Philips Achieva 3.0 T scanner (Philips, Best, the

Netherlands) equipped with a head-coil. Echo-planar (EPI) T2*-weighted images with

blood oxygenation level-dependent (BOLD) contrast were acquired. Scanning parameters

were: repetition time 2000 ms, echo time 3.7, flip angle 90°, field of view (FOV) 240.00

mm, matrix size = 128 x 128, pixel size 1.9 x 1.9 mm. Each functional run lasted 260

seconds. Thirty-six axial slices of 3mm thickness were collected in each volume, with a

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gap thickness of 1mm. Slices were selected to cover the dorsal surface of the brain and

include the cerebellum ventrally. A high resolution, 3-dimensional T1-weighted image

consisting of 170 axial slices was acquired of the whole brain to facilitate anatomical

localization of activation for each subject.

6.3.2.3 fMRI Data Analysis

The functional MRI data were pre-processed for each subject, using Brain Voyager

(Brain Innovations, the Netherlands, www.brainvoyager.com) trilinear interpolation for

3D motion correction and Sinc interpolation for slice time correction. No temporal or

spatial smoothing was performed on the data. The data were then further motion

corrected with MCICA, a computationally expensive but highly accurate method for

motion correction [25].

The Brain Extraction Tool in MRIcro (http://www.sph.sc.edu/comd/rorden/mricro.html)

was used to strip the skull from the anatomical scan and first functional image from each

run to enable a more accurate alignment of the functional and anatomical images. Custom

scripts in Amira software (Mercury Computer Systems, San Diego, USA) were used to

co-register the anatomical and functional images.

Manual segmentations to obtain ROIs were based on anatomical landmarks and guided

by a neurological atlas [26]. Sixteen ROI’s, hypothesised to be involved in motor tasks,

were drawn separately in each hemisphere. They were outlined on the unwarped, aligned

structural scan for each subject using Amira software. The ROIS are: primary motor

cortex (M1) (Brodman Area 4), supplementary motor cortex (SMA) (Brodman Area 6),

prefrontal cortex (PFC) (Brodman Area 9 and 10), caudate (CAU), putamen (PUT),

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thalamus (THA), cerebellum (CER) and anterior cingulate cortex (ACC) (Brodman Area

28 and 32). The labels on the segmented anatomical scans were resliced at the fMRI

resolution. The raw time courses of the voxels within each ROI were then extracted.

Since the task frequencies were too fast to be directly measured with the sluggish

Hemodynamic response inherent in BOLD fMRI signals, a block design was used for

analysis. A hybrid Independent Component Analysis (ICA) / General Linear Model

scheme was used to contrast each of the 2-frequency blocks with the static force blocks

[27] and create statistical parametric maps (SPMs).

6.4 Results and Discussion

This section presents the results of applying our proposed fMRI spatial analysis technique

on the synthetic and real data described in Section 6.3.

6.4.1 Validation on Synthetic Data

6.4.1.1 False Positives as a Function of Bandwidth

The bandwidth, L, is the main parameter of the proposed SPHARM approach. The first

synthetic example was designed to analyze effects of varying it on the false positive rate

of the proposed method. Two samples of were obtained with no signal added

(only noise). SPHARM-s features were derived for each of the ten binary ROI masks in

. SPHARM-fs and SPHARM-f features were then derived for each of the 10 synthetic

ROI fMRI activation statistics for the two samples of . These features were then

analyzed as explained in section 6.2 to obtain a p value. Since Rmax for these sets was

found to be 19 voxels, the number of shells used was set at 40 (6.7). The bandwidth used

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to obtain all the SPHARM features was varied over a range and at each value, 100 such

experiments were performed.

Knowing that no difference exists between the two groups, we were able to decide if the

resulting p value from the permutation test was a false positive or not. was set at 0.05

and any p value below this threshold was declared a false positive. The graph so obtained

between the false positive count and the bandwidth used is shown in Figure 6.3.

Figure 6.28 False positive rates using SPHARM-f features for various values of the parameter L (Bandwidth). .

Figure 6.3 clearly shows the stabilization of the false positive rate (FPR) well before the

theoretical bandwidth of 36 is reached. A FPR of 3 in a 100 trials is below the expected 5

counts at the set alpha value, confirming FPR control.

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6.4.1.2 Comparison with ROI-N

For this example, two samples of were created, One with no signal (only noise)

and another with a known non-zero signal value, SNR was controlled by the magnitude

of delta (Section 6.3.1). Figure 6.4 plots the average SNR value in the signal group

against the delta value. Results for both the SPHARM and the ROI-N approach were

recorded for increasing SNR values. The results are depicted in Figure 6.5 and Figure 6.6.

Figure 6.29 The average SNR plotted against increasing delta value.

Figure 6.5 summarizes the performance of the two SPHARM approaches. SPHARM-fs

features are able to discern a difference in the two groups at -3.4402 dB and higher SNR

values. SPHARM-f features perform better, picking up the difference at an SNR value of -

10.7674 dB.

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Figure 6.30 Sensitivity of the SPHARM approach. The mean Euclidean distance between the feature vectors of a group with only noise and of another group with increasing SNR is plotted against the SNR. The star and triangle markers denote distance which yielded a

p value less 0.05, signifying that the method detected differences between the groups.

Figure 6.6 presents the results of the ROI normalization approach for different height

thresholds for the absolute value of the t-statistic. Hayasaka et al [23] have shown that

results are sensitive to the height threshold and cluster size threshold used, both of which

are dependent on the estimated smoothness of the data. Based on their simulation results,

we use a very liberal cluster size threshold of 4 connected voxels (in a 26 voxel

neighborhood) corresponding to zero smoothness. A height threshold of 2 is also

considered liberal since the corresponding uncorrected (for multiple comparisons) p

value is 0.0304 with 18 degrees of freedom.

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6.4.1.3 Discussion

This example clearly shows that for the realistic pattern used, the sensitivity of both the

SPHARM approaches outperforms the ROI-N method. SPHARM-f features perform

better than SPHARM-fs features indicating the advantage of the principal component

subspace approach in reducing intersubject structural variations. The graphs for both

SPHARM methods show a consistent trend emphasizing the robustness of the method to

noise. The ROI-N method on the other hand, shows a higher susceptibility to noise,

especially by the t>|3| graph in Figure 6.6.

Figure 6.31 Sensitivity of the ROI-normalization approach. The number of voxels surviving various height thresholds is plotted against the SNR. A cluster size threshold of 4 connected voxels was used in each case. These results were computed from the exact

same data generated for Figure 6.5.

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6.4.2 Application to Clinical fMRI Data

Section 6.3.2 presented the real data that was analyzed using both the SPHARM

approaches (SPHARM-fs and SPHARM-f) and the ROI normalization approach.

6.4.2.1 Results of SPHARM analysis

SPHARM-fs and SPHARM-f features were derived for all participants as outlined in

section 6.2. Table 6.1 presents the maximum radius and bandwidth used for each pair

(left and right) of the Sixteen ROIs analyzed. Values for each ROI were obtained

considering all twenty participants. All SPHARM-f features were obtained using a

subspace with d=3 (10) of the SPHARM-s PC subspace.

Table 6.9 Maximum radius of ROIs and the corresponding bandwidth used

ROI RMAX Bandwidth

ACC 16 30

CAU 11 20

CER 19 36

M1 15 28

PFC 16 30

PUT 6 12

SMA 16 30

THA 8 16

Table 6.2 displays the result of the SPHARM analysis. For each ROI, permutation tests

were performed for both SPHARM features comparing the two tasks performed at

different frequencies. Each p value indicates the result of the permutation test (N=10,000)

with an alpha value . The table only shows ROIs for which at least one test was

153

found to be significant. ROIs in the left hemisphere have a ‘L_’ prefix, while those in the

right hemisphere have a ‘R_’ prefix.

Table 6.10 SPHARM analysis of the two frequency tasks. Only ROIS with at least one significant result are shown

ROISPHARM-fs

Normal

SPHARM-f

Normal

SPHARM-fs

PD

SPHARM-f

PD

L_CER 0.0613 0.4694 0.0239* 0.0202*

L_M1 0.1767 0.1761 0.0863 0.0104*

L_PFC 0.5302 0.9497 0.1045 0.0378*

L_THA 0.1200 0.0425* 0.0651 0.2513

R_CER 0.0546 0.1599 0.0478* 0.0309*

R_PFC 0.6938 0.5273 0.0150* 0.0166*

R_THA 0.0914 0.1057 0.1602 0.7946

6.4.2.2 Results from ROI Normalization

The Sixteen ROIs from the twenty subjects were also analyzed using the ROI-

normalization approach. Both tasks were performed in the same session enabling the

same anatomical T1 ROI to be used to obtain corresponding functional maps. Hence the

normalization template obtained was used to warp both tasks fMRI activation statistics

(Section 6.2.4). Due to the uncertainty regarding the best height and cluster size threshold

to be used, we used a range of height thresholds varying from 2 to 5 in steps of 0.5 in t-

statistic magnitudes, while using a cluster size threshold of 4. Among the thirty two

combinations of tests performed (2 subject groups with 16 ROIs each), only the left and

the right cerebellar hemispheres in the PD subject group had at least one cluster left after

the thresholding.

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6.4.2.3 Discussion

These results demonstrate that using the standard ROI normalization approach, increased

movement rate was associated with an increase in activity of the cerebellum bilaterally in

PD subjects, but not in age-matched, healthy controls. This is consistent with an

increased reliance on visual feedback in PD subjects mediated by the cerebellum [28].

Using the SPHARM-fs features also identified a change in the shape of activation within

the bilateral cerebellar hemispheres of PD subjects, and in addition was able to detect

changes in the activation of the ipsilateral prefrontal cortex of PD subjects. This region is

associated with performance monitoring [29], thus a change in the activity of this area

may reflect an increased attentional demand in PD subjects as the movement becomes

more difficult.

The SPHARM-f approach, in which structural variations in ROI anatomy across subjects

are minimized, sowed greater sensitivity to changes in BOLD activation features during

increased movement speeds. Specifically, control subjects showed a change in the

activation of contralateral thalamus with increasing movement rate, consistent with an

increased output from the basal ganglia. PD subjects were apparently not able to adjust

the output through the thalamus, and instead showed adjustments in the output from

bilateral cerebellum, bilateral prefrontal cortex, and contralateral M1 in response to

increased task demands. Increased activity of M1 and cerebellum in PD has previously

been suggested to be a compensatory mechanism [30, 31]. It is thus possible that

compensatory mechanisms are recruited during tasks which make greater demands on the

motor system, and rely on changes to the shape as well as the level of activation.

155

6.5 Conclusions

In this paper, we proposed a new technique for analyzing spatial activation patterns in

fMRI data using 3D SPHARM features. These features were obtained by intersecting 3D

data distributions with concentric shells of increasing radii followed by a radial

transform. Our other main contribution was a novel approach to account for anatomical

shape variations across subjects while discriminating subtle changes in spatial

distribution of fMRI activation patterns within an ROI. The effectiveness of the proposed

approach in mitigating structural variability, robustness to noise and comparative

sensitivity were validated on synthetic data. We also applied this approach to discriminate

functional pattern changes within anatomical ROIs in fMRI data collected. Using this

approach, we were able to demonstrate differences in the way that PD subjects and

healthy controls respond to an increased task demand, reflecting failure of PD subjects to

increase basal ganglia output, and a reliance on cerebellar and cortical activity to enable

successful performance. This adjustment may reflect a compensatory mechanism in PD

subjects.

An interesting application of this approach would be to compare activation patterns

between two subject groups that are expected to have systematic changes in both

structural and functional aspects. Avenues to decouple these aspects in the feature domain

would yield promising new directions in fMRI data analysis.

156

6.6 References

[1] K. J. Friston, A. P. Holmes, K. J. Worsley, J. B. Poline, C. Frith and R. S. J.

Frackowiak, "Statistical Parametric Maps in Functional Imaging: A General Linear

Approach," Human Brain Mapping, vol. 2, pp. 189-210, 1995.

[2] F. Crivello, T. Schormann, N. Tzourio-Mazoyer, P. E. Roland, K. Zilles and B. M.

Mazoyer, "Comparison of spatial normalization procedures and their impact on

functional maps," Hum. Brain Mapp. (USA), vol. 16, pp. 228, 2002.

[3] O. T. Carmichael, H. A. Aizenstein, S. W. Davis, J. T. Becker, P. M. Thompson, C.

C. Meltzer and Y. Liu, "Atlas-based hippocampus segmentation in Alzheimer's disease

and mild cognitive impairment," Neuroimage, vol. 27, pp. 979-990, 2005.

[4] M. Ozcan, U. Baumgartner, G. Vucurevic, P. Stoeter and R. Treede, "Spatial

resolution of fMRI in the human parasylvian cortex: Comparison of somatosensory and

auditory activation," Neuroimage, vol. 25, pp. 877-887, 4/15. 2005.

[5] C. E. Stark and Y. Okado, "Making memories without trying: medial temporal lobe

activity associated with incidental memory formation during recognition," J. Neurosci.,

vol. 23, pp. 6748-6753, Jul 30. 2003.

[6] A. Geissler, R. Lanzenberger, M. Barth, A. R. Tahamtan, D. Milakara, A. Gartus and

R. Beisteiner, "Influence of fMRI smoothing procedures on replicability of fine scale

motor localization," Neuroimage, vol. 24, pp. 323-331, Jan 15. 2005.

157

[7] B. Thirion, P. Pinel, A. Tucholka, A. Roche, P. Ciuciu, J. F. Mangin and J. B. Poline,

"Structural Analysis of fMRI Data Revisited: Improving the Sensitivity and Reliability of

fMRI Group Studies," IEEE Trans. Med. Imaging, vol. 26, 2007.

[8] M. I. Miller, M. F. Beg, C. Ceritoglu and C. Stark, "Increasing the power of

functional maps of the medial temporal lobe by using large deformation diffeomorphic

metric mapping," Proc. Natl. Acad. Sci. U. S. A., vol. 102, pp. 9685-9690, Jul 5. 2005.

[9] P. A. Yushkevich, J. A. Detre, D. Mechanic-Hamilton, M. A. Fernandez-Seara, K. Z.

Tang, A. Hoang, M. Korczykowski, H. Zhang and J. C. Gee, "Hippocampus-specific

fMRI group activation analysis using the continuous medial representation,"

Neuroimage, vol. 35, pp. 1516-1530, May 1. 2007.

[10] R. T. Constable, P. Skudlarski, E. Mencl, K. R. Pugh, R. K. Fulbright, C. Lacadie, S.

E. Shaywitz and B. A. Shaywitz, "Quantifying and Comparing Region-of-Interest

Activation Patterns in Functional Brain MR Imaging: Methodology Considerations,"

Magn. Reson. Imaging, vol. 16, pp. 289-300, 4. 1998.

[11] A. Nieto-Castanon, S. S. Ghosh, J. A. Tourville and F. H. Guenther, "Region of

interest based analysis of functional imaging data," Neuroimage, vol. 19, pp. 1303-1316,

2003.

[12] D. Kontos and V. Megalooikonomou, "Fast and effective characterization for

classification and similarity searches of 2D and 3D spatial region data," Pattern

Recognit, vol. 38, pp. 1831-1846, 11. 2005.

158

[13] B. Ng, R. Abugharbieh, X. Huang and M. J. McKeown, "Characterizing fMRI

activations within regions of interest(ROIs) using 3D moment invariants," in MMBIA,

2006.

[14] D. V. Vranic, "An improvement of rotation invariant 3D-shape based on functions

on concentric spheres," in 2003, pp. III-757-60 vol.2, 2003

[15] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, 23-25 June 2003, pp. 156-65, 2003.

[16] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs. volume:

Invariant shape descriptors for 3D region of interest characterization in MRI," in ISBI,

2006, pp. 754-757, 2006.

[17] A. Uthama, R. Abhugharbieh, A. Traboulsee and M. J. McKeown, "Invariant

SPHARM shape descriptors for complex geometry MR region of interest analysis in MR

region of interest analysis," in 2007, pp. 1322-1325, 2007.

[18] G. Burel and H. Henocq, "Three-dimensional invariants and their application to

object recognition," Signal Process, vol. 45, pp. 1-22, 1995.

[19] D. M. Healy, D. N. Rockmore, P. J. Kostelec and S. Moore, "FFTs for the 2-Sphere-

Improvements and Variations," Journal of Fourier Analysis and Applications, vol. 9, pp.

341-385, 2003.

159

[20] Y. Zhang and A. M. Martinez, "Recognition of expression variant faces using

weighted subspaces," in Proceedings of the 17th International Conference on Pattern

Recognition, ICPR 2004, 2004, pp. 149-152.

[21] Y. S. K. Vetsa, M. Styner, S. M. Pizer, J. A. Lieberman and G. E. -. Gerig, Caudate

Shape Discrimination in Schizophrenia using Template-Free Non-Parametric Tests. , vol.

2879, 2003, pp. 661-669.

[22] J. Ashburner and K. J. Friston, "Nonlinear spatial normalization using basis

functions," Hum. Brain Mapp., vol. 7, pp. 254-266, 1999.

[23] S. Hayasaka and T. E. Nichols, "Validating cluster size inference: random field and

permutation methods," Neuroimage, vol. 20, pp. 2343-2356, 2003.

[24] D. H. Brainard, "The Psychophysics Toolbox," Spat. Vis., vol. 10, pp. 433-436,

1997.

[25] R. Liao, J. L. Krolik and M. J. McKeown, "An information-theoretic criterion for

intrasubject alignment of FMRI time series: motion corrected independent component

analysis," IEEE Trans. Med. Imaging, vol. 24, pp. 29-44, Jan. 2005.

[26] J. Talairach and P. Tournoux, Co-Planar Stereotaxic Atlas of the Human Brain: 3-

Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme, 1988,

[27] M. J. McKeown, L. K. Hansen and T. J. Sejnowski, "Independent component

analysis of functional MRI: what is signal and what is noise," Curr. Opin. Neurobiol.,

vol. 13, pp. 620-629, 2003.

160

[28] J. F. Stein and M. Glickstein, "Role of the cerebellum in visual guidance of

movement," Physiol. Rev., vol. 72, pp. 967-1017, Oct. 1992.

[29] A. M. Owen, A. C. Evans and M. Petrides, "Evidence for a two-stage model of

spatial working memory processing within the lateral frontal cortex: a positron emission

tomography study," Cereb. Cortex, vol. 6, pp. 31-38, Jan-Feb. 1996.

[30] S. Thobois, P. Dominey, J. Decety, P. Pollak, M. C. Gregoire and E. Broussolle,

"Overactivation of primary motor cortex is asymmetrical in hemiparkinsonian patients,"

Neuroreport, vol. 11, pp. 785-789, Mar 20. 2000.

[31] U. Sabatini, K. Boulanouar, N. Fabre, F. Martin, C. Carel, C. Colonnese, L. Bozzao,

I. Berry, J. L. Montastruc, F. Chollet and O. Rascol, "Cortical motor reorganization in

akinetic patients with Parkinson's disease: a functional MRI study," Brain, vol. 123 ( Pt

2), pp. 394-403, Feb. 2000.

161

7 Conclusions and Future Work

7.1 Technical Contributions

This thesis presented a novel spherical harmonics based framework for region of interest

shape and functional analysis of neurological MRI data. We first introduced an invariant

spherical harmonic representation to characterize 3D real valued functions. Unlike

previous methods [1, 2], which were invariant to rotation, scale and translation of the 3D

function, the method proposed here ensure that the features are also unique. We achieved

this additional uniqueness property by proposing the use of a radial transform on a shell

based representation of 3D real valued functions. This ensures a one to one

correspondence between the 3D real valued function and the SPHARM representation, an

important requirement for any feature based representation.

We then proposed the use of these features to discriminate shape changes in anatomical

regions of interest in brain magnetic resonance imaging data. Unlike previous approaches

which studied the 3D surface based representation [6, 7], we used these features to study

shape as represented by the 3D volume representation of the regions. The surface based

representation methods have a serious limitation of not being able to characterize regions

with concavities [7] or regions without spherical topology [6]. Our features do not place

any restrictions on the allowable topology, vastly increasing their potential. Synthetic

162

data experiments, closely modeled after real world observations were used to validate the

sensitivity of these features to subtle shape changes.

We then extended the use of these invariant features to study the spatial distribution of

activation values within a 3D region of interest in functional magnetic resonance imaging

data. This area of research is dominated by spatial normalization based voxel-by-voxel

analysis approach [9] which has been criticized for its various shortcomings [10, 11, 12].

Feature based analysis of these regions has been proposed earlier [13] but an important

aspect, namely, accounting for intersubject variability in the shape of the ROI has not

been addressed. To enable the proposed SPHARM approach to sensitively detect changes

in the functional pattern of activation in 3D space, while being relatively robust to

structural changes in the shape of the ROI, we proposed a novel principal component

subspace approach. Using synthetic experiments modeled after real world observations,

we were able to show the superior sensitivity of this approach when compared to a

recently proposed alternate feature based approach [13] and also to the current state-of-art

spatial normalization approach in analyzing functional MR data.

In summary, the contributions of this thesis are:

1. Translation, rotation and scale invariant properties of spherical harmonics were

augmented to include the important property of uniqueness, a limitation of

previous approaches.

Uthama A, Abugharbieh R, Traboulsee A, McKeown M.J, “Invariant SPHARM

Shape Descriptors for Complex Geometry in MR Region of Interest Analysis. In

29th Annual International Conference IEEE EMBS: 2007; Lyon, France; 2007.163

2. These features were used to characterize 3D volumes of region of interests (as

opposed to 3D surfaces) in the brain exposing interesting, clinically relevant

changes in the PD brain. Presented in:

Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer,

Mechelle Lewis and Xuemei Huang, “Shape (But Not Volume) Changes in the

Thalami in Parkinson Disease”, Submitted to BioMed Central Neuroscience,

2007.

Uthama A, Abugharbieh R, Traboulsee A, McKeown M. J, “Invariant SPHARM

Shape Descriptors for Complex Geometry in MR Region of Interest Analysis” , in

preparation.

3. Spherical harmonic features were used to characterize spatial distribution

properties of entire 3D volumetric fMRI data in region of interests. First

presented in:

Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ, “3D Regional fMRI

Activation Analysis Using SPHARM-Based Invariant Spatial Features and

Intersubject Anatomical Variability Minimization”, in preparation

4. A principal component subspace approach to reduce influence of anatomical

variations in feature based representation of fMRI data was proposed. Presented

along with clinical results in:

164

Uthama A, Abugharbieh R, Palmer S.J, Traboulsee A and McKeown M. J,

“Characterizing fMRI Activations in ROIs while Minimizing Effects of

Intersubject Anatomical Variability”, in preparation.

7.2 Impact on Neuroscience Research

The spherical harmonics features developed were first used to study the shape of 3D

volumes of specific regions of the brain. Structural MR image were obtained for both

normal subjects and subjects afflicted with Parkinson’s disease. The use of spherical

harmonic features revealed shape changes in the thalamus and the brain ventricles in

subjects with Parkinson’s disease. These changes correlate well with previous

pathological (post-mortem) observations [3]. This demonstrates that our proposed

approach is a promising and powerful alternative means for neuroscientists to non-

invasively observe such changes in vivo.

The SPHARM framework developed for functional analysis was shown to have higher

sensitivity than the leading (normalization-based) competing approach; it was able to

detect clinically relevant changes in the functional response of PD patients. The

improved sensitivity of the spherical harmonics achieved using principal component

subspace projection enabled the detection of what is hypothesized to be a compensatory

mechanism [4, 5]. These changes would not have been detected using the current state-of-

art approach, thus underscoring the impact of the improved sensitivity demonstrated by

our approach on the clinical inferences drawn from functional MR data.

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7.3 Future Work

The SPHARM based MR analysis framework of ROI data presented here has potential

for further investigation. Some key directions include:

Given that the SPHARM features are valid for any 3D real valued function; this

framework can be easily extended to analyze other MR data. Some key modalities

where this could be beneficial include characterizing and discriminating scalar

measures extracted from diffusion tensor (DTI) imaging data such as fractional

anisotropy (FA).

Further study into the core of the SPHARM representation might help localize the

global changes now observed, to a more local description. This will help make

better clinical inferences by being able to isolate parts of the ROI responsible for

the observed change.

Since the proposed features can handle disjoint ROIs, further investigations can

be carried out by analyzing sets of ROIs simultaneously. This could potentially

shed more light on the functional connectivity between different regions.

The main advantage of the proposed framework is its generality due to the ease with

which this method can be used to perform group discrimination analysis on any real

valued 3D data. We expect this method to reveal more interesting clinical

observations from MR data, which would have a significant impact in neuroscience.

166

7.4 References

[1] M. Kazhdan, T. Funkhouser and S. Rusinkiewicz, "Rotation invariant spherical

harmonic representation of 3D shape descriptors," in Symposium on Geometry

Processing, 23-25 June 2003, pp. 156-65, 2003.

[2] D. V. Vranic, "An improvement of rotation invariant 3D-shape based on functions on

concentric spheres," in 2003, pp. III-757-60 vol.2, 2003.

[3] J. M. Henderson, K. Carpenter, H. Cartwright and G. M. Halliday, "Loss of thalamic

intralaminar nuclei in progressive supranuclear palsy and Parkinson's disease: clinical and

therapeutic implications," Brain, vol. 123 ( Pt 7), pp. 1410-1421, Jul. 2000.

[4] S. Thobois, P. Dominey, J. Decety, P. Pollak, M. C. Gregoire and E. Broussolle,

"Overactivation of primary motor cortex is asymmetrical in hemiparkinsonian patients,"

Neuroreport, vol. 11, pp. 785-789, Mar 20. 2000.

[5] U. Sabatini, K. Boulanouar, N. Fabre, F. Martin, C. Carel, C. Colonnese, L. Bozzao, I.

Berry, J. L. Montastruc, F. Chollet and O. Rascol, "Cortical motor reorganization in

akinetic patients with Parkinson's disease: a functional MRI study," Brain, vol. 123 ( Pt

2), pp. 394-403, Feb. 2000.

[6] D. Goldberg-Zimring, A. Achiron, S. K. Warfield, C. R. G. Guttmann and H. Azhari,

"Application of spherical harmonics derived space rotation invariant indices to the analysis of

multiple sclerosis lesions' geometry by MRI," Magnetic Resonance Imaging, vol. 22, pp.

815-825, 2004.

167

[7] S. Tootoonian, R. Abugharbieh, X. Huang and M. J. McKeown, "Shape vs. volume:

Invariant shape descriptors for 3D region of interest characterization in MRI," in ISBI,

pp. 754-757, 2006.

[8] Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ: Invariant SPHARM Shape

Descriptors for Complex Geometry in MR Region of Interest Analysis. In 29th Annual

International Conference IEEE EMBS: 2007; Lyon, France; 2007.

[9] K. J. Friston, A. P. Holmes, K. J. Worsley, J. B. Poline, C. Frith and R. S. J.

Frackowiak, "Statistical Parametric Maps in Functional Imaging: A General Linear

Approach," Human Brain Mapping, vol. 2, pp. 189-210, 1995.

[10] F. Crivello, T. Schormann, N. Tzourio-Mazoyer, P. E. Roland, K. Zilles and B. M.

Mazoyer, "Comparison of spatial normalization procedures and their impact on

functional maps," Hum. Brain Mapp. (USA), vol. 16, pp. 228, 2002.

[11] M. Ozcan, U. Baumgartner, G. Vucurevic, P. Stoeter and R. Treede, "Spatial

resolution of fMRI in the human parasylvian cortex: Comparison of somatosensory and

auditory activation," Neuroimage, vol. 25, pp. 877-887, 4/15. 2005.

[12] F. L. Bookstein, ""Voxel-based morphometry" should not be used with imperfectly

registered images," Neuroimage, vol. 14, pp. 1454-1462, 2001.

[13] B. Ng, R. Abugharbieh, X. Huang and M. J. McKeown, "Characterizing fMRI

activations within regions of interest (ROIs) using 3D moment invariants," in Computer

vision and Pattern Recognition Workshop, pp 63, 2006,

168

[14] Martin J. McKeown, Ashish Uthama, Rafeef Abugharbieh, Samantha Palmer,

Mechelle Lewis and Xuemei Huang, “Shape (But Not Volume) Changes in the Thalami

in Parkinson Disease”, Submitted to BioMed Central Neuroscience, 2007

[15] Uthama A, Abugharbieh R, Traboulsee A, McKeown M. J, “Invariant SPHARM

Shape Descriptors for Complex Geometry in MR Region of Interest Analysis” , in

preparation.

[16] Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ, “3D Regional fMRI

Activation Analysis Using SPHARM-Based Invariant Spatial Features and Intersubject

Anatomical Variability Minimization”, in preparation

[17] Uthama A, Abugharbieh R, Palmer S.J, Traboulsee A and McKeown M. J,

“Characterizing fMRI Activations in ROIs while Minimizing Effects of Intersubject

Anatomical Variability”, in preparation.

169

8 APPENDIX

All data obtained and analyzed during the course of this thesis was obtained from human

subjects after due consent was obtained. The studies were approved by the concerned

ethics review boards. This appendix lists the ethics approval certificates obtained from

the University of British Columbia Clinical Research Ethics Board.

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171

172

173